Question

Arianna kicks a soccer ball off the ground and into the air with an initial velocity of 42 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach?

Answer 1

Assume it is kicked straight up at 42 ft/s. That is the value of "v", the upward velocity, and s would be zero (assuming the ball was on the ground).

H(t) = –16t² + vt + s = –16t² + 42t + 0
solve for t when H(t) is zero (at the start and at the end),

0 = -16t² + 42t = t(-16t + 42)

This is true only for t = 0 (not important) and when -16t +42 = 0
or t = 2.625 seconds. But that time is equally split between going up and coming down (you assume there is no air resistance).

So the maximum height is reached for t = 2.625/2 = 1.31 seconds.

The maximum height is given by the equation H(t) = –16t2 + vt + s
H(1.31) = -16(1.31)² + 42(1.31) = 27.6 ft.