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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

Verified Answer :

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

Answer: 159 ft.

Blacklash

Answer:

Maximum height reached = 159.25 feet

Step-by-step explanation:

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

At maximum height derivative is zero.

That is

        \(\frac{dh}{dt}=-32t+100=0\\\\t=3.125s\)

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

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