How To Solve Amazon's Hanging Cable Interview Question
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- Опубліковано 2 сер 2024
- A cable of 80 meters (m) is hanging from the top of two poles that are both 50 m from the ground. What is the distance between the two poles, to one decimal place, if the center of the cable is (a) 20 m above ground? (b) 10 m above ground?
Chatterjee, Neil, and Bogdan G. Nita. "The hanging cable problem for practical applications." Atlantic Electronic Journal of Mathematics 4.1 (2010).
euclid.trentu.ca/aejm/V4N1/Cha...
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I don't want to sound hyperbolic, but this problem is actually a "cinch" if you think about it. Thanks for 5 million views in 1 year! (Perhaps the most watched math video of the last 12 months on UA-cam, you guys are awesome!)
Some doubts
*(1)* If the lowest part of the cable is 20m, the catenary equation is y (x) = 20.cosh (x / 20). Hence, as y (x) = 50, we have 20.cosh (x / 20) = 50, ie x = 20.acosh (5/2), or rather x is approximately 31.33m. Therefore, the distance between the posts is 62.66m. Furthermore, using the arc length formula, we arrive at half the length of this catenary at L = 20 senh (31.33 / 20), ie approximately L = 45.81m. What would give as total length of the catania: 91.62m.
In short: if the shortest distance from the wire to the ground is 20m and the wire describes a fixed catenary on the 50m poles, the length of this cateraria is NOT 80m but 91.62m.
*(2)* Assuming the length of the wire is 80m, and we do not know the parameter "a" ... Then, using the arc length in half of the catenary, we find senh (x / a) = 40 / a. And, since y (x) = 50, we would have "a" . cosh (x / a) = 50, hence cosh (x / a) = 50 / a. Using the fundamental relation we find (50 / a) ^ 2- (40 / a) ^ 2 = 1. Hence, a = 30. Using this value, we deduce that cosh (x / 30) = 50/30, ie x = 30 *.acosh (5/3), or approximately x = 32.96m. Hence, the distance between the posts would be 65.92m.
In short: if the wire length is 80m, the shortest distance from the wire to the ground cannot be 20m. It should be 30m.
Where am i going wrong?
Note: Sorry for my English. =)
@@icarovidalfreire2209 ya know i didn't understand anything but ig u r right
@@thefirminator Didn't you understand because of my english or why there are any errors in my calculations? 😅😂
Whether we could not consider the line as parabola
Psychopath
The official answer to the question is, "Dude, I'm here fore the box folding job. You got me confused with the cable hanging guy."
W Mcg lol
Lmao
W Mcg 👏👏👏👏🍾🍻
Youre fuckin hired bruh
Lmao
Hahaha
The actual answer was, "I would measure the distance using a tape measure I bought on Amazon."
Answer is 30 meters bro
@@factswithsatish - I think you missed the joke, bro.
Same would i do
A Fluke laser distance meter is the most accurate.
You're hired, sir.
I think part (b) is a clever interview question, as it requires some outside the box thinking, but part (a) doesn't seem very practical unless they expect you to only approximate the answer. I doubt that most mathematicians know the equation for a catenary from memory. To be honest if given this question I would probably just approximate the cable with a parabola and hope that the answer is close enough.
I sort of just solved part (b) by looking at the thumbnail and i was like - wait a second! it's 0 meters
honestly you can even just approximate it with triangles and that's pretty close. All you need is the pythagorean theorum. That gets you to 26.46, which I would probably round up to 27 since we know there's bend in it that will make it longer than a straight line. And if you do this with the second one you'll get the correct answer of 0.
@@NotMyActualName_ that's exactly how I tackled the problem, but keep in mind that you would actually want to round the number *down* for this scenario! Since the straight line would reach further, compared to a curved line of the same length, the maximum distance decreases as you increase the curvature.
I think using the Pythagorean theorem for a quick "off the top of your head" reply (acknowledging that it's only an approximation) is a better alternative, as long as you later can refer to Google and other sources to solve this with the proper equations (which I could never remember by heart, and even if I did, I should not trust that blindly, and would have to double check with trusted sources anyway before taking any kind of important decision).
It still is a cool math problem though!
@@bibliophile4292 i think that the picture was misleading) it is better only to read the task
I looked at it for a bit a figured I could get close enough with C²-A²=B² and ignoring the tangent might be fine. So I figured A=Height from top of pole to center cable B=Half distance between poles C=Half cable length. I got A²=1600 & C²=1600 and then when, wait - what? Distance between poles is 0? I better finish this video.
Then there were all these crazy formulas & I was like damn I must have really messed something up in my reasoning but in the end for 10m version my 30sec solution actually was right.
But for 20ft height I would've said 50ft apart and been off by 4.6ft
In the interview, I would say we approximate the cable with a line and take x = SQRT(1600 -900) = 26.45. We then multiply by 2.
You can also easily see that the second one will be infeasible because it gives us zero distance.
Wait why 1600 and 900?
@@williamsorensen3958 Pythagoras theorem, both sides ^2
It is rather x = SQRT(1600 + 900) = 50 and multiply by 2
@@andriyOshtuk ???
give zero more distance?so you caculation is more correct??
I am a mechanical designer of 0ver 30 years, been to lots of job interviews, and was hired by many different companies, and I never once encountered any problem like this in any of my interviews. That Amazon would use such a problem in an interview seems totally absurd. Does Amazon hire overhead power transmission line engineers?
@@abcxyz2927 No these are for the programmers and software developers I would imagine.
My question is if Amazon even pay the people it hires after this level of interviewing questioning anywhere close to what they are worth?
@@smasherblues5322 50 meters from the ground, 0.5mm tall. Also, they're actually airhooks, not poles.
This is like the Google aptitude test that came out ten or fifteen years ago. It's basically an IQ question. Amazon wants to hire smart people.
The answer is unbelievably simple. No math required. (Hint: the picture is misleading you. Ignore the picture and simply consider the values.)
This is how Amazon delivery drivers work out how to throw your package over your back garden
😂
That would be a parabola, though. Not a catenary.
This is way underrated.
@@guepardiez Not at all. It is called dropping things from a height of 40 meters.
🤣🤣🤣
For the 10 meter case, if you draw a straight line from the top of one support to the lowest point of the cable, its length has to be less than 40 meters since the cable is a curve. Draw a horizontal line from that lowest point to the same support. Then you have a right angle triangle with a hypotenuse which is less than one of its sides. So the picture, as drawn cannot make sense. The only case which is feasible is when the cable has no curvature, i.e. it is vertical up and down. So the two supports have to be coincident.
That sounds like the way to answer the question without pulling out an obscure formula.
@@nighttrain1236 Yes.
And even then it requires an infinitely thin cable, which means it has zero mass, which, combined with the fact that it has no curvature, means it won't curve as it gets pulled down. The most logical explanation for it having a single lowest point is that the cable is a straight diagonal line to the middle, which means you can use a much simpler formula: you're basically calculating one side of a triangle. For the 10 meter case the answer now is possible, but this also changes the answer for the 20 meter case. We have a triangle with a diagonal side of 40 meters and a vertical side of 30 meters, this gives us a horizontal side of 26.46, for a total distance between poles of 52.9.
I used the exact same approach
When drawing the diagram at 4:33 you can see that cable is 40m to the center and the pole is 40m above your x-axis, which intuitively doesn't work. Visually you can see that x would have to be 0. But who would stand 2 poles beside each other and hang a cable between.
I want to meet the people who got this question right during the interview and still ended up working for Amazon.
Hi
@@henrymiller4136 lmfao
You don’t have to Ans to get a job btw
Depends if they found what they are looking for you are hired (not vise versa even if you Ans ?
Lol, this is not an interview for a dead end job. These people were not interviewing to deliver boxes.
This kind of problem is asked in tech interviews, so it would be for software engineers, data scientists or mathematicians. They are for jobs that pay over 100k a year as initial salary.
The selection process is usually composed of several interviews. These are not the "talk to someone in HR" interviews. They usually consist on problems designed to test the technical skills of the participants. This kind of interview process is standard in big tech companies, google, apple, facebook, amazon...all the big tech companies follow this type of process.
Pretty sure this question is for designers/mechanical engineers and not software engineers.
Sounds similar to the question they gave me; "if the bottle we need you to piss into is in the passenger footwell and you are strapped into the driver's seat of a standard delivery vehicle, at what angle of inclination do you need to aim to manage to get most of it into the bottle?"
7 degrees my friend. Unless it is greater than a 16oz bottle.
@@Evilthx Fahrenheit or Celsius?
@@ThatLegendary Kelvin My friend
@@Kingkhan-og8xw No, my name is Patrick
@@ThatLegendary Nah Kelvin is my friend
Asking this question out of the blue is like testing whether someone loves mathematical history.
I know a catenary from a parabola, but is all I remember about math at this point in my life. Years ago I took the GRE and got tentatively accepted to a graduate math program, but if one doesn't use it, one loses it. These are great refreshers.
When I got a job at Amazon all I had to do was say I could lift 30 lbs.
But, how do you KNOW the 2 poles only weigh 30lbs? ;-)
j miller- 60 lbs
50 lbs
Any lifting over 30 is assisted by special device invented by autistics
Now they just test how long you can go without using the bathroom.
As an accountant I would just ask what they want the distance to be.
Ouch!
As an accountant I also agree with the other accountant ..
As a person who employs an accountant, this is the correct answer.
Can you do my annual tax return please?
Lol
I'm a naval architect so I've come across catenary problems many times with anchoring. I have written numerical methods that solve it (because in this day and age it's quicker.
Then I saw the 1st problem at the end and instantly saw that they must be zero distance apart. If it wasn't after 10pm I would have done what you did and taken 10m from the bottom and come to the same conclusion
This is a catenary problem and can be solved easily by using basic integration.
how?
My high school math teacher warned that a catenary is not a parabola. The famous Gateway Arch in St Louis a catenary, not a parabola. People make this mistake because they have had elementary algebra but not hyperbolic functions, so they think it's x-squared.
@@michaeljarosz4062 Every physics students learn the calculus of variation in their classical mechanics course. Where they solve this hanging chain problem by using Euler-Lagrange equation.
Yes, but.....not everyone is a physics student!
I agree
If you can solve this problem in a few seconds, then they know you're able to deal with a fifteen second bathroom break twice per shift.
Because it only takes 15 seconds to change your diaper.
That you also have to ask permission to take, right?? Lmao that place is unreal.
Fifteen seconds? What, do you think money grows on trees? Clean your Reusable Amazon Warehouse Employee Diaper (TM) in your washer/dryer when you get home.
You don't have to take bathroom breaks if you don't eat or drink while you're working
Damn you guys have a really bad view of Amazon
I guess I wouldn't have gotten the job, no wonder why they don't have same day delivery anymore..lol.
Here's the generic solution:
Catenary equation: y=a*cosh(x/a)-a+h
take the derivative and plug into the arclength integral...
dy/dx = sinh(x/a)
L = int(sqrt(1+sinh(t/a)^2),t,0,x) = int(cosh(t/a),t,0,x) = a*sinh(x/a)
square this equation then use identity (cosh(x)^2 - sinh(x)^2 = 1) to rewrite.
L^2 = a^2*sinh(x/a)^2 = a^2*(cosh(x)^2 -1)
now manipulate and square the catenary equation...
y-h=a(cosh(x/a)-1)
(y-h)^2 = a^2*(cosh(x/a)-1)^2
Now divide the catenary equation by the squared arclength equation...
(y-h)^2/L^2 = (cosh(x/a)-1)^2/(cosh(x/a)^2-1)
using the exponential form (definition) of cosh(x) you can rewrite the right side...
(y-h)^2/L^2 = (cosh(x/a) -1)/(cosh(x/a)+1)
define b=(y-h)^2/L^2
and solve above equation for cosh(x/a)
cosh(x/a) = (1+b)/(1-b)
Plug this back into the original catenary equation...
y = a*(1+b)/(1-b) -a +h
and solve for a...
a = (y-h)*(1-b)/(2*b)
because we know cosh(x/a) = (1+b)/(1-b), and we know a and b, we can solve for x.
x = a*acosh((1+b)/(1-b)).
Warped Perception of you knew 10,000 equations you’d be alright. Don’t worry dude I mean yeah you have to be a genius to do this but you don’t have to do this to be a genius.
Jess Stuart yeah that’s why I changed majors
It took me about 45-60 seconds of thinking, but I'm nearly positive I know the answer, at least to problem b. But a would require more math than I'm willing to do right now. Though, if I'm not mistaken the shape the cable would make is a hyperbola. *Edit:* Almost right. :-) I was definitely right on b.
Eric Hopper So what's the answer
•The best thing I've found so far! I found this when looking for actual, demonstrated use of hyperbolic functions. The amazon, 10 meter "trick" was just a bonus.
•I was never taught hyp trig (nor heard of it until I saw it on a calculator function), but I know regular trig well, so why gap my knowledge here?
•Most others' videos are just a list of applications or some diagram without much real, how do you *use* it explanation (and where does hyperbolic angle come in, how is it linked to e^x functions in growth /interest rates, other not so obvious applications etc etc).
Explanation is perfect, thanks for taking us through the math and giving us more sources to look through!
Everyone: *begins using trigonometry*
Me, with a tape measure: "Where the poles at?"
It depends how many times I wrapped the cable around their neck
😂😂😂😂
Did you pull it up really tight till the light dimmed in their eyes?
Hahahaha!!! Too funny. Well played.
That's quite sadistic. Are you an accountant?
Lol
I was worried about replacing my high-end older oasis with this one ua-cam.com/users/postUgkxCgPI5O2AtmcHq9SJhgsCGbpAzJAJfrJp but it is surprisingly light and the screen resolution is just as good. I never had the warm light on my old kindle, but i do not use it on the ipad so I will probably not need it. I think the only thing I'll miss is the self-adjusting light, but this is so worth it!
am glad i made it in 3-5 seconds using pythagoras square triangle formula. i knew it was an approximate but i soon noticed square of hypothenus was equal of square of the pole length, it is 40^2. then the other side should be 0 in length !! or pythagoras had been tricking me for my entire life ! lol ! thanks ! ayala & yami, shamanes associate
exactly....if both sides are the same length, they must be side by side.
But the hypothenus isn´t equal to the square of the "pole length"? the pole length is still 50m. 😂
But we can measure the length of base of the triangle...
When he got to the term "cosh" I bailed and went searching for funny cat videos. Don't laugh...I know my limitations.
haha...lol. THAT was funny :-)
I thought your ‘cosh’ was a typo. Til I got there in the video.
I’ll be enjoying funny cat videos with you.
@@julianndavis9415 i love this comment of urs, (wait for me).
Hyperbolic cosine
Is it supposed to be cos h? I'm confused
Edit: nevermind. It's hyperbolic cosine
Broke Mathematicians: hyperbolic cosine
Woke Mathematicians: C O S H
As we here (Czech) call sine fully "sinus", I tend to call sinh "sinhnus". "Hnus" means disgust, as well as something disgusting. Such as sinh :-D
@@lautheimpaler4686 Nikal lawde, pehli fursat mai nikal
Illuminati 33 lmao Harry Potter spell
Osh cosh b'gosh
Wealthy mathematicians: DOSH
Interesting use of hyperbolic trigonometric functions. I would have stated the cable sag is somewhat negligible and used the Pythagoream Theorem and doubled it. It gives like a value of 52.9 meters. The last part was easy, and I concluded it was zero because the cable just sags down on either side to just 10 meters above the ground. Basically, I turned this into a triangle problem and solve from there.
Someone posted this on Facebook and after I figured it out to be 0 m, I found this video to see how other people processed the question. The way I processed it:
Half the cable is 40 m, which is half the 80 m cable and also 50 m - 10 m = 40 m. So if I keep raising the bottom by 10 m until I get to the 50 m height of the poles, then eventually I get to 0 m for half of the cable. So the poles are 0 meters apart which is nonsense regarding the actual picture. lol
Me: Solves the problem
Amazon: You're hired. Pay is 12 dollars an hour, mandatory unpaid overtime and no healthcare.
Also. Here's your piss bucket and don't be late
Amazon's minimum wage is $15/hour and its illegal to pay less than time and half for any hours worked over 40 in a week. Amazon is bad but not that bad
@@subatomicparticle r/wooooooosh
Is 12 dollars or 15 an hour bad? Thats more than what I earn in my country lol and I have a "decent" position working as a financial analyst. And everyone makes similar to that..
@@ave3360 in usa a financial analyst starts at $20/hr up to $50/hr or more
The poles are 12742km apart
at one decimal place, they said :-)
No its not that much. The answer is near 100
@@FlyFishingChronicles 20,000 km - You're about right, if you're flying. Walking would likely be a bit further (unless you're Jesus of course).
@@rumi9005 I believe you because you said Jesus.
@@paulgoogol2652 - You know my friend Jesús Fuentes? That's quite a coincidence, Paul.
Like many others have commented, I calculated the answer as two hypotenuses. Considering that this question was asked in an Amazon interview withouot concern for higher math, I must assume it was designed as a practical application of 8th grade geometry.
Quick approximation would be Pythagoras. a²+c²=c². We know one side with the pole height(30 resp 40 meters) and the hypothenuse with cable length/2 as 40. That means for cable hanging in the middle at 20m we have 40²=30²+b² which can easily be solved
Omg I did that too I thought I was wrong
me too!
I interviewed people for 6+ years at Amazon. I never once used this type of question. None of my colleagues ever used this type of question. We were never trained to use these types of questions (the training actually encouraged us to dig deep into actual candidate experiences related to the area we were hiring for). Only one time did I ever even hear of someone at Amazon using this type of question in a phone screen, and it struck me as odd because this is not the kind of interviewing Amazon conducts. So PSA: don't assume this is the norm.
I believe companies rely on knowledge tests to much and miss out on the people who have natural talent to do or learn better than someone who has all the right answers. Thinking out of the box is a talent that you can't get out of a book.
@@webyankee6558 To add to this, I'm a scientist myself, but I don't memorize any of these kinds of formulas. If I use something frequently for a time I might, but that's it. Pretty much any kind of formula needed is readily available with a quick search on the internet, or in a book, etc. That's the benefit of technology. If I were the hiring manager, I would care more about one's ability to use the resources available to them to solve such a problem than the fact they memorized formulas to look smart.
Amazons first question during the interview….
“Can you breathe on this mirror?”
“Ah, ha.. i see you in the mirror and the moisture confirms you are alive.”
“You are hired”
I worked for Amazon and was never interviewed, idk why. Maybe they just really needed people.
@@webyankee6558 this problem relies on someone memorising a formula. There is a way to solve it using physics from first principles (force balance along cable) but without being given values for, presumably, a spring constant, you could only derive general solutions.
I've been a software engineer for almost 30 years. Anybody who asks me this kind of nonsense gets smacked with twisted tea.
Agreed
Seriously!
Well, but if we ask you to draw this in an interactive chart, with one pole able to move sidewards, you are back to business ? The answer to the original question will only be a side-output then.
How is this a non sense?? If you don't know or like Maths, does that make this useless? Humanity's tech keeps rolling only because these are people who know Maths very well.
@@yashsvidixit7169 No sorry, it's nonsense to memorize a formula you need once every 10 years. This ist old fashioned thinking to store everything in your head.
It's allowed to use "external storage" like Wikipedia to look up, when needed.
I mean, some exaggerate and need a calculator to compute 5*7. But computing 312*28 in your head, you can do for party entertainment to impress people, no job should depend on that ability.
This is great. I teach physics and from part a, without really doing any math, I guessed it would be around 50 using a flawed thought process of using the pythagorean theorm, which 45.4 rounds up to. But with part b, before I thought about how to work out the problem, I thought to myself, "why is the cable so far down? That makes no sense," and I didn't have a mathematial guess for myself. So seeing you explain it all is pretty funny.
Good point, I'm not a math expert at all, but also the fact it droops down over half the radius. It is an elliptical, half would be 25m, so it droops with 20m left. So the shorter diameter part of the elliptical (idk the correct term for this) connects the two poles. If it drooped 25m, it would be 50m apart, but it falls a little longer at 30m, so the poles are less than 50m apart, and probably not too much more. From that alone one could guess btwn 40-48m or so.
Very interesting. I tried to solve the B problem applying the pythagorean theorem to the triangle having the hypotenuse between the center of cable and the pole. This led me to the absurdity that the cathetus was greater than the hypotenuse itself. In fact, if the cable is 10m from the ground then the cathetus lenght is equal to the distance between the minimum point of the cable and the anchor point that is 40m. Since the cable is 80m, the half curve between the minimum point and the anchor pount has a lenght of 40m and subtends the hypotenuse that cannot be more than 40m. So we will have a hypotenuse that can at most be equal to the cathetus. We therefore do not have a triangle but two overlapping segments, for which the poles coincide. Then i have seen the catenary equation, that is something you cannot have in memory as well and you have to study or approximating with a parable. Amazing but not amazon.....
I’m never going to mess with an Amazon delivery driver again.
again? do tell...
The people that answer this get a different job,
@@beau6113 I think that’s the joke
@@beau6113 Exactly. Most likely, this isn't a required Q & A to be a delivery truck driver. Yet you should always be courteous to anyone who provides you a service you're too lazy [not in the case of disabilities or other hindrance] to go to the store & get yourself. Kind of like a sit-down diner, restaurant or bar. 😁
Very wise of you.
But it's not just the smarts.
Like River Tam, they can kill you with their brains.
Amazon: "Entry level programming position"
Also Amazon: "10 years of experience required"
As someone who interviewed with Amazon for an entry-level programming position, this is false.
@@SpideyNinety08 Well you didn't say if you got the job or not so how could we believe you? 🤣
Thanks for solving the puzzle. Now you can start filling boxes in an Amazon warehouse near you. 👍
Who else thought of using the Pythagorean Theorem here, treating the cable as the hypotenuses of two right triangles, with their bases being a horizontal line tangential to the lowest point of the cable. This may not be as accurate, since we're simplifying a curve into a straight line, but it should be a good approximation and Amazon would probably still appreciate our approach to the problem.
Yes I tried this originally at first. Even though a simplification you can still find the trick that when you work out the numbers, the vertical and horizontal lengths of this triangle would both be 40, so we know something is up, and deduce the other length must be 0. I kind of got to here but didn’t think it was a trick question or say 0. Still glad I could actually think of that though lol.
Before watching the video, I did exactly that and got 0 as a result. I thought I was wrong because of the thumbnail, only after I opened up the video and saw the image was made by the channel and that it was not provided with the question I understood what was going on
I found a slightly quicker method. I got a friend to help me with 2 50m long poles with an 80m long cable attached at the top of each pole. Then another friend measured the distance of the drop of cable in the centre between the 2 poles I and my friend were holding. Once it reached the required height from the ground we just measured the distance between the 2 poles! Easy and certainly quicker than doing the maths...
The answer for both is less than 80 feet.
Are you superman or the flash?
@@mraj9002 Bring my friends along obviously! I will get extra credit for thinking outside of the box...
@@xenomorph6961 You wouldn't get the job. They only want to pay people from the neck down. They don't want you thinking outside the box or anywhere else. They just want you to fill the box with product and send it to a van.
Ha but if you were asked the amazon question of 10m..you can solve it easily with zero maths in about 2 minutes. Meanwhile you'd still be playing with many friends, rented in construction equipment to erect two 50m poles! (Hint buy 60m poles so you can have at least 10m in the ground..and about 20 bags of postcrete mix!)..perhaps you could scale down and use 2*5cm drinking straws and an 8cm bit of string! But still..the answer is zero!
If I were asked this question in an interview, I'd just linearize it and use Pythagoreans. ~53m.
Paul Amsden me too
JKay11235 yeah but Paul said linearize which means your answer is an approximation. I disagree with the answer because linearizing shows you that part b is just not possible because it's an impossible triangle, but it's still a fine start to a problem if you don't have random shitty formulas memorized
JKay11235 that's why it would only be an estimation dumbass. Don't know why Amazon would expect people to be familiar with hyperbolic functions if they're just going to be moving boxes all day.
ShakingBabies5ever alternatively, look up the degenerate triangle.
Shraydn ok I have done so. To my understanding, it's just a specific triangle that serves the same purpose and yields the same result as thinking of it as a line in this case. The line is oriented directly downward if you want to be extremely specific
I guess the proper solution of 20m version should include deducing the exact function that describes the curve, based on forces of gravity and tension working on a unit of wire, and then taking an integral.
The curve is... a hyperbola. That's the common starting point here. As MYD points out, you just need to look up the equation for a hyperbola and solve it at the known [x,y] coordinate for the constant.
@@kindlin how do you know it's a hyperbole? It's your assumption.
You must deduce the formula itself, this is the essence of the problem. The rest is just calculation a monkey can do.
@@kindlin Isnt that a parabola? Hyperbola would never touch the axis'
@@phobics9498 Unfortunately a cable does not hang in a parabola, that's more like projectile motion, as a classic example, a parabola is much easier to work with. No, a uniform, prismatic, tension-only cable takes the shape of a catenary, which is mathematically defined with the hyperbola. It does still have a closed-form expression, tho, so there is that.
EDIT: A prismatic member has the same shape and material along its length; so, it's redundant with uniform in my list, as the the definition of prismatic means a _uniform shape_ and a _uniform material_ along its length. Anyways, I just had to clarify that.
Yeah i find that way more interesting. This can be "easily" solved by taking the langrangean (or hamiltonian) of the system and obtaining the stable points, wich would indeed be described by an hyperbolic function. Then, it's just a problem of describing the initial conditions of the system.
if you can answer this question why are you applying at amazon
Because AI took our jobs! 🤷🏻♂️😅👉🏼🤖
“Sinch”, and “cosh”. I’m gone
It’s actually pronounced “shine”
Stfu it’s a sin hyperbolic function
That’s why I hate geometry
@@c.o2307 Sean Connery is that you?
Sinh not sinch
oh darn, you mean; Amazon, the airplane engineering company, I thought you meant the online department store.
Amazon soon will be all things to all humans.
6.3 million of the 6.4 million viewers had the same idea ;)
Hah, me too. I thought it was an interview for admins to see how they reacted under pressure. 😂
I thought about Amazon forest🤣😂
As did I. Commented elsewhere, but it seems deliberately misleading. Principle of my argument stands.
If you can answer this question, you are way overqualified to work at Amazon.
I got similar results from considering the sagged cable to be in perfectly still environment as a semi circle (180 degrees of a circle with 160 M circumference) with the bisected midpoint 20 m off the ground for my mental image. Then I overlaid the Pythagorean Triangles to orient the poles & radius of the Semicircle. I calculated by hand solving for B or Radius & confirming by plugging the values for either the B side from Pythagoras Method into the Circumference Formula (C = 2πR) where 160 m as C is known & 3.14 for pi.
The second problem was a problem from the mental image because even changing the curve to a parabola opening UP, the gross measurements of the beginning diagram were not possible to have both the length of the cable stay at 80 m & the poles 50 plus the limiting factor of a 10 m gap from the ground. Before getting into harder math it was clear the original diagram had to be altered.
I am certain this was more of a "how do you handle a stressful situation" exercise, problem -solving skills & communication exercise plus perseverance & the measure of out-of-the-box thinking.
I think it's important (at least for me) to understand the "how" & "why "of answers of one cannot recognize an figure that may be orders of magnitude wrong.
I don't ever want to have to calculate Sine & Cosine even with a slide rule & found the simpler methods enough.
Finally, a normal guy
nice!
... They're asking this as an interview question? For what? This is something I used to give as a homework problem for advanced freshman physics. I can't imagine what it would tell you in an interview setting.
I can't imagine answering it
Yonatan Zunger it tells you the same thing it tells you about your freshman student. It tells you who can think, not just crunch numbers. BTW, I didn’t realize it either, so I guess I’m not as smart as I sometimes like to think I might be.
I suspect that (barring the fact that this was a trick question), the point of asking these questions isn't to see who gets it right, but the method people use to try to solve it. If someone just immediately throws the towel into the ring it tells you something useful (and you probably wouldn't hire them). If someone gets as far as splitting it at the centre and the coordinate system, but then doesn't know the right equation for the cable, of if they take some time to approach the problem in another organized way it tells you something about how they think. Someone actually immediately solving it would actually be a disappointing result, as all it tells you is that the person was familiar with the question.
Ummmm this is for the airplane engineering company called Amazon, not the online department store
Don't give our bald master new ideas
The fact that it’s using hyperbolic functions just reminded me I should probably brush up on those if I’m ever gonna hope to apply to ucsd
sooo... your answer to "how to solve the question" is: look up the formula online. great job! I learned a lot in this video.
I’m a senior in mechanical engineering and have never used hyperbolic trig functions in my life. Seen them obviously, but no one uses them lmao
Amen
lucky you, i used them a lot in quantum mechanics.
God of Moisture J
God of Moisture Your name is hilarious.
cable problems, beams on elastic foundations are a few places in mech engr hyperbolic trigs are used.
I kinda arrived at this conclusion due to first simplify the problem (ignoring any curvature and assume the cable is straight and bends once) effectively turning the problem into a triangle problem. Now I didn't think this would do anything but give me an approximation to work with, but an immediate problem based on this approach (involving the need to only look at half of the diagram) you have a right-angled triangle, where you know that the height is 40m, but the hypotenuse line (across from the 90 degree angle) also is 40m (the longest the cable can be, since it is under no curvature). That is of course impossible, unless they are the same line and it is not a triangle at all but a straight line. Which means the problem, only works if 2 poles is one pole and no distance and no area can be in between. Effectively arrive at the answer. Lucky maybe, but works.
Actually, I did the same before watching the video. Then I tried doing it for case a) and got a different value, but it's comprehensible when you think about it: if you have actual distance between the two poles, there is a curvature in the center of the hanging cable, but if the two poles are together/only one, that curvature doesn't exist, thus making the two right-angled triangles approximation actually accurate.
@@cloud_strife8 If you solve case a assuming the cable is two straight lines, then use pathogens theorem, the answer you get is within 0.2 meters satisfying the requirement to be within one decimal place.
I started typing this in, as I did the same, but then saw you got that, too. I wouldn't call that lucky but smart way to simplify a problem for approximation, which is very helpful in many cases. @william meek: It's not that accurate here: For the 20m case that gets to 40^2 - 30^2 = x2, i.e. about 26.5m, which is not very close but gives a first idea. Closer is assuming the cable as lower half of an ellipse. Circumference U is approx. pi * [ 3 (a+b)/2 - sqrt(ab) ] with a and b being the longest and shortest half diameters (admittedly had to look that up, too, but this equation is a bit simpler than the one from the video. If a = 50-20 = 30m, then, filled in, b = 20.4m, i.e. 40.8m distance between poles.
@@christophstegert8386 ya the whole "get within x percentage accuracy" kinda tricks people into thinking they have to use some method to approximate the curve and calculate a number. EVILLLLLLL hehe
It works to a degree. The longer the distances the larger the error. For this problem simple Pythagoras gets you to the solution very quickly and easily.
for the b variation im pretty sure you can solve it using the pythagorean theorem because the pole is 40 meters high and the length to the center is 40 meters so 40 squared minus 40 squared is 0
How? You can only use the pythagoras thereom for right angled triangles
As someone who taught geometry at one time and took refresher courses in multivariable calculus, I only watched the intro to the video, stopped it and calculated then watched video. The cable 20 m above the ground approximates two hypoteni (the plural of hypotenuse) of right triangles, which would make each hypotenuse 40, one side of the triangle is the pole from 50m to 20m which is 30 m and which would make the width of the middlle of the cable about 26.5 m from each pole by the Pythagorean Theorem x =sqrt(40^2 - 30^2) = 26.5 m. So it's about 53 m from pole to pole.
That is in the ballpark of the calculation in the video, which is so complicated it requires trig functions and the quadratic equation, that I don't think there would be time enough to do in a job interview unless you were being interviewed for an engineering position and were given a test, not an interview.
The 10 m is a trick question. In order for the cable to be 10m off the ground, there would be no distance between the poles because half the length, 40m would hang down from 50m height of each pole accounting for all 80 m of cable
Mickey Cashen just because u took time I’ll like ur comment
That's what I came up with.
But the trick in the question for a) is precisely that you're asked for it to be correct to a decimal place, which means that linearising the curve would not work. You can see that because your answer is not even correct to the first significant figure. Even part b), because it's asking to a certain number of significant figures, makes you start trying to calculate. Which is obviously why it's a trick, and requires simple addition to solve if you think to picture it.
ive seen it on instagram, i think its exactly a question for hiring engineers. i dont wanna sound cocky but i had it in like 5 minutes. these kind of calculations is what you do on a daily basis in all kinds of engineering classes.
Mickey Cashen That’s what I’m sayin...
Saying "kosh" and "cinch" can be classified as incitement to self-harm in my opinion
Really?
Brings back bad memories of high school maths?
If you visualize that same scenario I arrived at a close answer for the 20m based off using the 10m gap and estimating. If you increase the distance of those poles until the cable is taught then it would be approximately 95-100m your example of 20 somewhat confirmed that by estimating it at 90.8 with a 20m sag.
I'm glad I didn't wasted more than a minute to try to solve this problem and moved on to see the solution because I would have never solved this problem.
Wow. I never realized that packing boxes in trucks was that difficult. Guess I won't be working at Amazon any time soon.
Amazon dont do interviews this is for bigger promotions
rob1248996 / this isn’t for people that work in labour, this is for people doing difficult work like finance
@@d6853 Finance requires you to know the distance between two poles? No wonder the DOW is so artificially high.
@@rob1248996 It may be for engineers working on AWS. That would make sense, then.
that’s right! spot on
You can estimate the 20m situation with Pythagoras. You end up with a right triangle of legs 30m (50-20 for the pole), x, and a quasi-hypotenuse of 40m. 40m is longer than the actual hypotenuse, because of the curvature of the cable - it does not follow the straight line distance between the top of the pole and the midpoint of the cable. But let's say we say "I don't know the caternary formula, by Pythagoras gives me a good first estimate." I think that's reasonable.
30^2 + x^2 = 40^2. 1600 - 900 = x^2. x = sqrt of 700, which is about 26.45m. The actual hypotenuse being shorter than 40m, you would say 26.45m (times two to get 52.9m) represents an effective upper bound on the answer.
To get a lower bound, assume the cable has infinite mass and infinite tensile strength, such that it immediately droops to 20 meter off the ground, and then stretches parallel with the ground before reaching the other pole. Now you have a rectangle, with an x distance of 40 meters across (80 - 20x2 for each drop). So you can say for certainty that the distance must be between 40m and 52.915m. And the actual value of 45.4m ends up pretty well smack in the middle. Not exact, but quick, and not bad for basic math.
Mike B 😂😂 that was my go to assumption. Too bad the margin was that huge for a single decimal answer.
My answer was also similar
Works like a charm for solution B though
- Glad I'm not the only one who over thought it.
@@guillaumegaudin694 I mean yeah because you're just squaring and square rooting it
I'm a mechanical engineering technologist - great video! But I do have a question (aside from the strange fact that Amazon asks this when they don't deal with overhead power lines).
How about using the parabolic equations y= a(x-h)^2 + k, where h=o (horizontal displacement of the parabola from the ground), and k=10 or 20 (vertical displacement from the bottom of the rope to the ground)? What's the reason behind Cosh and Sinh?
Cheers
The shape formed by the rope is not a parabola, even though it looks like one - it's called a catenary, and the equation for it is that one involving cosh
@@gisopolis77 👍
The task with 2 50m poles and 80 m cable hanging 10 m from ground has trivial solution. - the poles are next to each other with no space between them.
"Fool us once, shame on you. Fool us twice, shame on us. Fool us 3 times we take you to the parking lot and kick your ass" (Penn Jillette, 2018)
😂
Amazon: "Please solve this problem."
Interviewee: "This problem is a sinh."
Amazon: "You're hired."
You need more likes cos you earned them :)
LOL, DTH. Back when I was at school, 'coshes' were OK, but sinh was pronounced 'shine'. How times have changed!
/me breaks out effing tape measure
like i said after you.. that kind of math is very unusual these days
Funny cus the curve can be modelled by cosh
I got the 0 for the second one pretty quickly, then tried to use a ratio to get the first one. This failed miserably because (it turns out) as the poles are pushed closer together, the center of the rope is not dropping at a linear rate.
My question is; Intuitively speaking, why does the center drop from a height of 50 to a height of 20 (3/4 of the total drop from 50 to 10), but the poles have traveled only from 80 apart to 45 apart (less than half their total distance)?
I would like to know what exactly the equation is that relates the distance between the poles to the height of the center point of the rope. (Or vice versa).
The equation may be in the video, but my understanding of hyperbolic functions is a bit hazy, and I do not see why a sagging rope is a perfect hyperbola.
Thanks!
Depends on what the cable is made of. A steel cable would stretch less than a rubber one. What does this have to do with repairing their delivery trucks?
God, „cosh“ and „sinch“ makes my toe nails hurt XDD
I find it VERY disturbing that you are the ONLY ONES (besides me there is only TWO) THAT SEEMS TO HAVE NOTICED THIS!
SMDH
Just watched this and heard him say “cosh” this made my day😂😂💀💀
what's wrong with cosh?
But sinch should be sinh
Were those meant to be sine and cosine?
@@derekw9724 no, they are meant to be cosh and sinh.
Those are the hyperbolic versions of sine and cosine.
en.wikipedia.org/wiki/Hyperbolic_functions
I have a 24" monitor, so the distance is 7.5" when in full screen mode.
that's actually a very smart solution. You could have measured the paper in some way during the interview.
And here i thought i was gonna use the Pythagorean theorem
for the 10m problem, i approximated the diagram into a rough right angled triangle with hypotenuse 40m and height 40m and hence came to the same solution in like 30 seconds
Congratulations, you got the job! Now, to the warehouse with you!
Who else decided to leave at the middle of the video but then decided to stay?
ME!
Lol
I let the video play and read the comments,now I don't know the answer and really don't care.
I just sped up the video
I fell asleep 1 minute into it, once the math equations were started.
I enjoyed this one! Thanks dear.
I got the same answer for 10 m using the Pythagorean Theorem...but what you say makes so much more sense!
Interesting. I took a totally different approach, by attempting to apply the pythagorean theorem, while chopping up the diagram into triangles, and I basically came to the same conclusion. The problem I ran into is that I thought I was doing something wrong, and never bothered to really look logically at the situation. For most of these kinds of problems, my number-one problem is confidence in my findings, and that's something I really need to work at.
I did not find the same answer using Pythagorean theorem. I got: 26.45751 times 2, which means 52 meters. I very doubtful about this video.
Yes that's what I did as well.
@@AlgoTradingX that's because the Pythagorean Theorem doesn't account for the curve at the middle of the cable. I went the same route initially but had a feeling that it would have a measure of noise because that theorem assumes perfectly straight sides.
Triangles don’t have curves…
Cut a piece of string 8in (or 8cm) long then cut 2 pieces of string 5 in long to represent the poles. Place the 8in string between them and move them together until the 8in string center is 1in up from bottom of the two 5in poles.
Our boy Fresh Taulocker is descending into madness.
For anyone wondering where the half-cable equation came from, it is derived by plugging the function modeling the cable into the curve arc length formula, with the bounds of integration being 0 and x with respect to t, and equating it to 40.
what level of math would you need to solve this problem?
Thank you for this. I did solve this with a book reference though It took a long time with lots of equations.
As a mechanical engineer, I would just use Pythagoras equation of a^2+b^2 = c^2 and call it a day, but good job factoring in the tangency!
But this is a serious underestimation.
That's so wrong
@@d.bcooper2271 Exact answer = 45.2m. Pythagorean triangle = 52.9m, estimate down to 50m which is off the exact answer by only 10%. We can do the exact stuff later, but in a job interview or a team discussion no one has catenary equations near them and they don't have to. That is how a real engineer does it in preliminary design.
It's a parabola
U gotta study class 11 again
Learn the meaning of "to one decimal place", "engineer".
nowadays, many interviews become a show of the interviewers.
I was actually wondering why such question is included on the interview, whereas this may be more appropriate for a test. Interview should focus more on the behavior quewtions and analyzing a candidate's employment history
Its a show off
But still, this question can help you find those who can think, instead of just crunching numbers. Moreover, being interviewed is also a show. So it's fair if the interviewer is playing the game too.
Pamm. No? Pamned... No? Pam mnd.... hello lady....
You shut up!!
It’s what happening when you give one side full power without regulations. Add your average student to a position like this and you have your circus show.
Laws must always protect the people first, then the interest of companies.
I had a similar interview question that wasn't quite as unpractical or unrealistic as this one. Mine was to determine how many laptops could be stored in the belly of an airplane for transit. Average plane, nothing military, commercial passenger aircraft. I needed to walk through my mental calculations out loud so the interviewer could hear my thought processes in arriving at an answer. By walking through what I'd experienced in the size of the laptop boxes, normal pallet size, and approximately how many pallets could fit underneath a plane, I got pretty damned close to the actual measured and calculated answer. In fact I was SO close to the actual answer, the interviewer was stunned. No one had ever been able to get that close just verbally walking through the variables.
Still didn't get the job...
Seems that we assume the poles are vertical, but if the 80m cable is strung taught and the poles are at an angle (11.5° @ 10m) then the distance between the base of each pole is 177.98m (80m(cable) + 48.99m(pole base to top @ 11.5° angle))
And 171.66m @ 20m from ground with poles leaning in at a 23.5° angle.
Also have to assume that the ground is horizontally flat..
I believe this is my first ever youtube comment in nearly 20 years...
I'm so disappointed that a mathematician broke out an applied engineering formula without deriving it. I've watched many of your videos and can't remember another instance of no derivation/proof. What you did was closer to Googling the answer than solving the problem.
Exactly. Looking up formulas from someone elses solution is not a solution. This video should be retitled 'how to apply formulas'.
I'm with you on this. This should have started with a proof showing that the cable-mass doesn't affect the shape.
Then derivation of the shape formula.
Congratulations on your first comment dude !
UA-cam is 15 years old if you start counting form the day the domain was registered.
The "cosh" and "sinch" are killing me XD
Am I the only one to say them "cos-h" and "sin-h" ?
i do... and moth mathematicians I know in Canada do.
Me too, it just makes more sense to me.
When he said cosh and sinch I was upset haha
I always said "cosh" and "shine".
THANK YOU!!!? OMG... the experts of today are imbeciles!
What software do you use to teach and bring equations and to move from one step to next? please let me know.
How is the cable attached to the pole? Who installed the poles? Are they plum? At that hight the pole is same diameter at the base and the apex? If not where was the pole to pole measurement taken from? Is the ground level or did someone shoot a bench mark for sea level?
I remember on NPR car talk, they had this same question with 75m poles and a 150m long cable and said how far apart does the poles need to be for the cable to just hit the ground. Needless to say my friends looked up some formulas for catenary and was dumbfounded when they got the answer
Alright, I misremembered the problem but here it is www.cartalk.com/node/44836
Still, same trick as the video
Would like to see Bezos solve it first.
He pays someone for that.
He can't solve a bung eye let alone math problems
@@defaultname01 He employs a lot of people from Harvard.
@@DrPepperJNL like an accountant 😂
You don't get smarter watching other people getting smarter. Bezos learned that.
LOL! My favorite G. W. Bush quote! You've made my day.
I saw the thumbnail and thought to myself…
If I was asked this in an interview; I’d say: “that’s close enough to a right triangle for me, we’ll just use a squared plus b squared”
And then when I did it on a notecard I found out that for the 10m problem the distance would be 0.
“Whoops guess I’m not as clever as I thought. “
Watched the video and was pleasantly surprised… By the end of it. Hahahahah great video, mate.
I'd just poop on the desk like a wild animal and run outta there
dyingggggggggggggggg lollllll
You're hired.
Eric Daniel lmao
Okay... THAT is Really Funny!
"Make that guy a sales rep!" ;-)
how did I get here, I was listening to pirates of the Caribbean theme song
I don't feel epic anymore
Anany Shrestth omg I died when I just read this hahahahh
Same. I literally just watched a vocal coach react to a song, and now im onto this
And i was watching the youtube rewind.
Anany Shrestth dre
Anany Shrestth lol😂😂😂😂😂👍
I got the 0 but wasnt sure if i was right. I approximated to a triangle with hypotenuse 40m (half the cable) and vertical side also 40m. Solving for the third side gives 0m, and both sides are symmetrical. Therefore there is 0m between the poles
HA! my lucky day! I actually saw the solution and thought about it then realized I'd never could solve it properly so I watched the rest of the video! :D
Tonight I will fall asleep with a proud smile on my face ... | )
No disrespect to my Amazon driver, but I'd be impressed if he solved this in an interview situation!
I did not know i was applying for a civil engineering position lol
Did you watch until the end of video?
@White Wolf true,but if im applying for a box handling postion this question serves zero purpose.
I figured it would be a question for high end positions, But if that question is for any and every applicant, that means If you Answer It Correctly, It will definitely will ring a bell , There's a purpose for it.
@@steventortora4487 The question serves to weed out people with freezing-point IQ.
@@steventortora4487 when box handlers put 40 pound kettlebells onto the wrong belts to where they fall off and kill a man(yes this happened) you start to consider the thinking ability of your employees
I must say, I feel pretty smart for figuring out the problem from just looking at the thumbnail.
Granted I completely forgot all the calculations for the first question after being out of education for just a year, but at least I looked at it before not calculating.
It took me 10s to solve it, very easy problem, but I've watched the video for the more generic answer you gave, very interesting. I had known the hyperbolic trigonometry at the time of the school, but now I don't remember almost nothing anymore.
Loved the G. Bush reference! " You can't get fooled again!" lol