Suppose a small cannonball weighing 16 lb is shot vertically upward with an initial velocity v_{0}=300 ft/s.

(a) Suppose air resistance is ignored. If the positive direction is upward, then a model for the state of the cannonball is given by d^{2}s/dt^{2}=−g. Since ds/dt=v(t) the last differential equation is the same as dv/dt=−g, where we take g=32 ft/s^{2}. Find the velocity v(t) of the cannonball at time tt.

(b) Use the result obtained in part (a) to determine the height s(t) of the cannonball measured from ground level. Find the maximum height attained by the cannonball.