Question

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t^2+90t gives the height h of the ball after t seconds.

a. Find the maximum height of the ball.

b. How many seconds will it take for the ball to reach the ground?

Answer 1

The ball reaches a height of 126.58 ft after 2.8125 seconds

Explanation:

The maximum height of a parabola can always be found by looking for the vertex. You can find the x value (or in this case the t value) of a vertex by using -b/2a in which a is the coefficient of x^2 and b is the coefficient of x.

-b/2a

-(90)/2(-16)

-90/-32

2.8125 seconds

Now to find the height, we input that value in for t

h = -16t^2 + 90t

h = -16(2.8125)^2 + 90(2.8125)

126.58 feet