Projectile motion with Mathematica

This note describes how to use the computer algebra system (CAS) Mathematica to analyse projectile motion with and without air resistance. For a projectile fired from ground level with an initial velocity ν ft/s at an angle θ degrees from the horizontal (0 < θ < 90°), it is well known that in the absence of air resistance, the projectile follows a parabolic path. However, this is not true if air resistance is taken into account. In the presence of air resistance, the equations of motion become complicated, thus making traditional handcalculation methods quite ineffective, and a powerful CAS such as Mathematica becomes an invaluable tool to better understand projectile motion. The note discusses how Mathematica can be used to create simulated experiments of projectiles with and without air resistance. These experiments result in several conjectures, leading to theorems.