Projectile Motion

A projectile is any object thrown into the air with some initial velocity (not purely vertical) and then left to move solely under the influence of gravity. Its path is called the trajectory. Everyday examples include an object dropped from a moving train, a bullet fired from a rifle, a ball thrown by hand, a javelin or shot-put released by an athlete, and a jet of water issuing from a hole near the bottom of a tank.

The key physical insight is that a projectile's motion is the combination of two completely independent motions: (i) a uniform (unchanging) velocity in the horizontal direction — since, with air resistance ignored, no horizontal force acts on it — and (ii) a uniformly accelerated velocity in the vertical direction, due to gravity. Two cases arise depending on how the projectile is launched: horizontal projection (the launch velocity is purely horizontal, §2.11.2) and angular/oblique projection (the launch velocity is at some angle to the horizontal, §2.11.3). Throughout, the standard simplify …