Question

A kicker kicks a football toward the opponent's goal line during a game. The ball begins its flight with an initial velocity of 70 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+70t+2
A. The answer cannot be determined.
B. 79 feet
C. 981 feet
D. 129 feet ...?

Answer 1

16t^2 + 70t + 2 -b/2a gives maximum height -70/-32 f(70/32) = 79 B. 79 Feet

Answer 2

h(t) = -16t^2 + 70t + 2
h'(t) = -32t + 70
0 = -32t + 70
32t = 70
t = 70/32
t = 35/16

Using either method, t = 35/16.
h(35/16) = -16(35/16)^2 + 70(35/16) + 2
h(35/16) = -16(1225/256) + 2450/16 + 2
h(35/16) = -1225/16 + 2450/16 + 32/16
h(35/16) = 1257/16
So the maximum height is 1257/16 feet, which is 78.5625 feet.

To the nearest foot, that's 79 feet.