Question

A kicker kicks a football toward the opponent’s goal line during a game. Theball begins its flight with an initial velocity of 90 feet per second when it is

kicked at a height of 2 feet by the kicker. To the nearest foot, what maximum
height will the ball reach?
You may use the function:
h(t) = – 16t^2+90t+2
A. 129 feet
B. 981 feet
C. 90 feet
D. The answer cannot be determined.

Answer 1

Maximum height reached = 159.25 feet

Explanation:

We have the equation h(t)=-16t²+100t+3

At maximum height derivative is zero.

That is

dh

---- = -32t + 100 = 0

dt

t=3.125s

Substituting t = 3.125 s in h(t)=-16t²+100t+3

Maximum height

h(3.125) = -16 x 3.125²+100 x 3.125 + 3 =159.25 feet

Maximum height reached = 159.25 feet