CS 3414 Problem Statement 4

A classic problem that can be modeled by ODEs is that of the motion of a projectile. Here is a simple example (taken from Faires and Burden, Numerical Methods, Brooks/Cole, 1998).

Suppose a ball of mass m=0.11 kg is thrown straight up into the air, with initial velocity v(0)=16 m/s. Assume the ball is slowed due to the force of gravity Fg = mg and due to air resistance Fr = -kv|v|, where g = -9.8 m/s2 and k = 0.002 kg/m. According to Isaac Newton, a reasonable model for the velocity of the ball at time t is

mv' = mg - kv|v|.

Note that velocity is positive when the ball is headed up.