Projectile Motion & Kinematics: How to Handle Projectiles Launched Diagonally

We solve for the horizontal range of a projectile launched at an angle from a cliff, using kinematic equations for constant acceleration. The key is to completely separate the vertical motion and the horizontal motion. In the absence of air friction (air drag) the vertical acceleration is 9.8 (m/s)/s downward and the horizontal acceleration is ZERO. The initial vertical velocity is the vertical component of the velocity vector. You can use trigonometry to find it; it is v0 multiplied by the sine of the angle above horizontal. Likewise, the initial horizontal velocity is the horizontal component of the velocity vector. It is typically v0 multiplied by the cosine of the angle above horizontal. A useful strategy is to use the vertical information to solve for the time of flight with a kinematic equation and then use the distance = rate x time in the horizontal direction to find the horizontal range. Again, the keys to success are to treat the horizontal and vertical motions independently and to follow sign conventions that are consistent with your choices of positive and negative directions.