Question

A kicker kicks a football toward the opponent's goal line during a game. The ball begins it's flight with an initial velocity of 100 feet per second when it is kicked at a height of 3 feet by the kicker. To the nearest foot, what is the maximum height the ball will reach? Use h(t)=_16t^2+100t+3

Answer 1

h=.5*100^2/32+3

Answer: 159 ft.

Answer 2

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)/(dt)=-32t+100=0\\\\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