Gravity and Vertical Motion Problem - Calculus
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- Опубліковано 28 сер 2024
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Gravity and Vertical Motion Problem - Calculus. In this video, a penny is thrown downward from a tower. We want to determine how long it takes to hit the ground.
Honestly, you are the reason I get A's in calculus! Thank you
For other calculus students still struggling with this, remember that when a question mentions the velocity due to gravity of something on Earth in FEET, you will always use -16t^2. This number is only for feet. So in the video when it gives you this question, you won't need to solve, just plug in the velocity above to the s(t) and proceed to find derivatives.
thanks alot patrick , for everything. i passed 3 levels of calculus because of your help. i never thought id ever pass calculus 1, let alone 2 other levels of it. lots of hard work and your videos are what go me through. thank you
The organization at the beginning was definitely a big help. Thank you!
PATRICK YOU ARE THE BEST.
Thank you much you helped me I will NEVER forget your help
You are right. It was very tedious.
@CobaltO18 He already has the function for acceleration, a(t) = -32. In order to find velocity, he must go backwards and take the integral of acceleration. Then he takes the integral of velocity to find the position function.
Thanks! This was a cool lesson. When your solving for the quadratic equation, couldn't you save yourself some pain and complete the square?
@cornboy3 99% of people i have met would rather poke themselves in the eye with a stick than to use completing the square
@patrickJMT Ha, thanks for the reply. I'd like to take the opportunity to thank you for all your videos. You got me genuinely interested in math after previously hating it. I've watched a lot of your videos now and am learning math recreationally in anticipation for studying for a maths degree at university this year. I know I'm only 16 and probably shouldn't try and bog myself down with all this, but it's just so damn fun and you make it a pleasure to learn!
I think it's pretty strange how you use 'feet per second'. Why not just use what everyone else uses and do it in meters per second?
@CobaltO18 Acceleration is the rate of change of velocity (which can be written as dv/dt or d^2s/dt^2). In this case, think of his function for acceleration as being dv/dt; since he wants to find v, he simply needs to integrate dv/dt to be left with v(t). I hope that makes sense, but I'm sure someone can explain it far better than I can.
@Skiddla A joke among chemists used to be that they'd make a spoon out of gallium, which has a very low melting point, and give it to each other to stir their tea with; of course once the spoon hit the water, it would melt and thus "disappear" into their tea.
How convenient! We're having a calculus test including this
thought you were going to play hangman for a second there :)
I don't see why people care what units he's using. The units are just an arbitrary choice for something like this since he isn't modelling a real-life situation. He could use lightyears if he wanted to, but he's just using the units he's most familiar with and uses most (as will be the case for most Americans), which is feet. With that said, fuck the imperial measurement system.
Lol, I had it right until I mixed a and c in the quadratic formula. Thank you so much for keeping it simple!
Oh, God! This is driving me NUTS! Is the penny being "thrown down" as you wrote, or is it being "dropped" as you said? There's a HUGE difference between the two! If the penny is being "thrown down," then force is applied by the person who is sending the penny to the Earth. If it's being "dropped down," then a lazy person is just letting gravity do its natural job...
Robert Doty Dude, chill. Like I said earlier, as long as the main point gets across, everything is fine. (Yes, I am aware that I accidentally used "acrossed" in my last comment. But hey, the main message was still present.)
I am geologist and I want to learn about this... this is important for me.. I am studying the Earth field..
Hassan Naser from Syria
my book and my teacher told me that velocity is the derivative of the location, and the acceleration is the derivative of the velocity, which would be the second derivative. why did u take the integral? im a little confused.
tnx
@Eiladel Of course you can just use one of your laws of motion for this, but I think the point Patrick's trying to demonstrate and illustrate is how these measurements and variables can be shown and manipulated using calculus. Obviously if you were asked to solve this you would just use the formula for displacement like you said, but that wouldn't make a very good calculus video!
I'm a little confused sir, why is it the acceleration is negative? As I recall, when a body was dropped downwards, it was accelerating because of gravity and my professor said that if it is accelerating, the sign should be positive. Similarly, if a body was thrown upward, the body will deccelerate as it reaches its maximum height and the sign will be negative. I'm a bit confused in that part. Thank you patrick, I appreciate all of your math vids, I hope you are my professor \m/.
IT'S ACCELERATION DUE TO GRAVITY. THE PENNY IS FALLING DOWNWARDS. NOT UPWARDS -_-
gravity is negative
All of the above are correct, but it really is a matter of perspective. Yes, gravity could be positive, but then everything else would be turned around. It's similar to velocity. Positive means going to the right, while negative goes to the left.
You the man!
@georgeda Why should that be a reason? I think it's stupid that the U.S.A's 'official' system of measurement still involves the archaic imperial units.
@Skiddla Yep, I read some fascinating stuff about the metric system in a book called "The Disappearing Spoon" which you might be interested in. It's tales about elements from the periodic table and talking about their interesting history and discoveries. It's interesting how they define a kilogram though... look it up. They made a cylinder from platinum and keep it locked up in a vault to keep it safe. That's what they define as a kilogram and is the only standard unit that's like that.
Thanks. It was so helpful.
this is quite cool but is there a place where you can use this but cant use suvat? (suvat is what i notate as those equations like s=ut+1/2at^2, not sure if you notate it the same)
You are an amazing teacher and are very helpful, thank you ! Coming from a future engineer : )
William Bartlett are you an engineer yet?
thanks mate
Is there any chance you could do a teeny, tiny video about calculating the moment of inertia with calculus? I can't seem to find an example clear enough for me to understand.
@OCNmeticadpa my thoughts, in word form : )
thanks fam
How can i determine speed when it reaches the ground?
Great video, but why oh why are you using the Imperial system!?
Is the gravity and vertical motion same as if you standing on high speed moving train?
hey im in grade 11 here in canada, and i was wondering cant you just use this to solve this problem?:
d = v (t) + (1/2) a t^2
this is a formula i use in physics and it seems alot simpler than all of this (unecessary calculus?).
i plugged in the values in the video and ended up with approximately 3 seconds. (is this video just showing how to use this calculus? or is an example in the real world?)
300 = 32t + 1/2 x 32 x t^2 ftw?
I love calculus even though I'm not taking calculus yet.
actually looks fun except the functions.
@billtruttschel Have it as a coefficient of friction my guess
4.31 second
man why are you making your life harder and using calculus. just use s=ut+0.5at^2
and use downward direction as positive
the point is to use calculus, good luck getting a zero.
i tried to use kinematics, got a wrong answer
Petty Officer Piggy Egg Head you must’ve made an error
@@pettyofficerpiggyegghead7240 Me too, why do you think that is?
can''t trust anyone whose typed words block the math
It's -16t squared. not -32.
Nevermind that's algebra.
I have to comment on this commercial for 'studypug'. It says "still using that video from 2006..." As if math has changed since 2006... hahaha Only the textbook and its price.
haha
Oh, God! Math majors! The tower is NOT "300 feet above the ground." If it were, the tower would be suspended in mid-air 300 feet above the surface of the Earth. I believe that what you meant to say is that there's a "300 foot-tall tower." Jeez! And you math-types so pride yourselves on accuracy! Learn the language, dammit!
Robert Doty Oh God! English majors! Why must you guys always criticize us math and science people? As long as the main point gets acrossed then the language is fine. I'm just messing with you. I like to mess with people who are good in literature and all that stuff.
It's not like you math and science people didn't criticize ME when I was taking math and science classes in college. Oh, noooooooo! I never was able to satisfy "you people" by coming up with a close approximation to the "one and only one" answer in physics class. Oh, no! It was NEVER "good enough" to say that the cannon ball would land "somewhere over there" once it was fired at a certain angle and a given initial velocity! No! You people wanted an exact distance (after ignoring air resistance). Well, Mister, now you're on MY turf! The English language will NOT be abused by the likes of you any more than you let me mangle Newtonian physics back in the day!
It's often said that "words matter." Ever heard anybody say that "physics matter?" Ever heard a girl say "Your physics REALLY turn me on!"? How about "You said some beautiful physics at your grandmother's funeral." Or maybe, "I LOVE the way that you integrate those equations! It makes me...HOT!" No, you haven't! Because that's not part of our colloquial dialogue!
So, suck it up math and science majors! This is the reason that we English majors always wind up with the girl at the end!!!
Robert Doty Wow. Dude, you need to chill. Teachers wanting an exact answer in class isn't a crime. It's a teacher's job to make sure your answers are precise and thorough. They're hard on you to help you to succeed. When I said that I mess with people who are good in literature, I meant that I did so in a harmless joking way.
Robert Doty Whoops. My last response to your comment was only in regards to the first half of it. Allow me to respond to the second half that began with me being on "your turf". First of all, it sounds to me like you have a strong connection to the English language. That's not a bad thing, but it can lead to people, such as yourself, wanting to criticize anything and everything that they deem grammatically incorrect. Second of all, the way you described how physics isn't used in occasions where proper language is used was correct. Physics is used for an even greater purpose. Physics is used to describe the inner workings of the universe and how everything interacts with each other. Finally, when it comes to the ladies, I think the ladies would prefer a smart and chill scientist such as myself rather than someone who wastes his time whining about English mistakes and complaining about physics class in college. Have a nice day.
Dude, I was joking. Jeez!