Question

The last answer is 1.5s and 56ft PLZ HELP PLZ

Answer 1

The ball takes 1.5 seconds to reach its maximum height

The ball's maximum height is 44 feet

Solution:

Given that,

The height in feet after t seconds is given by the function:

`h(t) = -16t^2+48t+8`

Let us first find the derivative of h(t)

Differentiate the given function with respect to t

`(dh(t))/(dt) = -16 * 2 * t+48+0\\\\(dh(t))/(dt) = -32t + 48`

At the maximum height the derivative of the function needs to be 0

`0=-32t+48\\\\-32t = -48\\\\t = (-48)/(-32)\\\\t=1.5`

Thus the ball takes 1.5 seconds to reach its maximum height

Find the ball's maximum height:

Substitute t = 1.5 in given function

`h=-16(1.5)^2+48(1.5)+8\\\\h = -16 * 2.25 + 72+8\\\\h = -36 + 80 = 44`

Thus ball's maximum height is 44 feet