Question

Stephen kicked a ball inside. The equation that represents the height h in feet of the ball after being kicked and elapsed amount of time t in seconds

Answer 1

The maximum height of the ball is: 14.0625ft

Explanation:

The missing information is:

`h(t) = 30t - 16t^2`

Required

The maximum height the ball attained

First, we calculate the time to reach the maximum height.

For a function:
`h(t) = at^2 + bt + c`

The maximum is:
`t = (-b)/(2a)`

So, the maximum of
`h(t) = 30t - 16t^2` is:

`t = (-b)/(2a)`

Where

`a = -16; b = 30`

So:

`t = -(30)/(2*-16)`

`t = -(30)/(-32)`

`t = (30)/(32)`

`t = 0.9375`

The maximum height is then calculated as:

`h(t) = 30t - 16t^2`

`h(0.9375) = 30 * 0.9375- 16 * 0.9375^2`

`h(0.9375) = 28.125- 14.0625`

`h(0.9375) = 14.0625`