Question

The height, h, in feet of a kicked soccer ball can be modeled by the function h(t) = -16t2 + 24t + 1, where t is in seconds. On its way down, the ball bounces off the crossbar of the goal, which is 8 feet above the ground. To the nearest tenth, when did the ball hit the cross bar?

Answer 1

Explanation:

let the height of a kicked soccer ball be expressed by the function:

h(t) = -16t^2 + 24t + 1 where t is in seconds

The ball hit the cross bar when the height is zero

The equation becomes

0 = -16t^2 + 24t + 1

16t^2 - 24t - 1= 0

t = 24±√24²-4(16)(-1)/2(16)

t = 24±√576+64/32

t = 24±√640/32

t = 24+25.298/32

t = 49.298/32

t = 1.54 secs

Hence the ball hit the cross bar at t = 1.6secs (to the nearest tenth)