Soccer Ball Velocity Question

Question

A soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by h(t) = —16t² + 32t, where t is time in seconds.

Determine how much time is needed for the ball to return to the ground.

Answer 1

Using the equation given, let H(t) =0, then 0 = -16t^2 + 32t. Solve this equation for t.

t (-16 t + 32) = 0.

The are two solutions: t = 0 and t = 2 sec. It takes 2 seconds to reach the ground.

A check on this is to use the relation Vfinal = Vinitial - gt, where Vfinal = 0 at the top of the trajectory. Solve for t = -32 ft/s / -32 ft /s^2 = 1 sec. As the time up equals the time down, the total time is 2 seconds as determined above.