Projectile Motion

As an example of motion in a plane we shall consider projectile motion: How balls, stones, bullets, and the like move after they are fired. Because we have yet to learn Newtons laws we start off with two assumptions which probably seem quite obvious and acceptable to you but which also follow naturally from Newtons laws. For projectile motion we have

1. motion with constant acceleration in the vertical direction:
2. Motion with constant velocity in the horizontal direction:

From these assumptions and what we know about kinematics we can write down expressions for the position vector in projectile motion:

where
 
Note that I have chosen the origin of my coordinate system to be at the point where the particle is at time t=0. This choice makes the formulae as simple as possible.

With these simple expression we can analyze an amusing little experiment.