Question

A stone is projected vertically upward from a platform that is 20ft high at a rate of 156ft/sec. Use h=−16t2+v0t+h0.Step 1 of 2: Determine when the stone will reach its maximum height. (Round your answer to two decimal places.)

Answer 1

h0 corresponds to the initial height, 20ft.

v0 corresponds to the initial velocity, 156ft/sec.

Then we get the following equation:

`h(t)=-16t^2+156t+20^{}`

To find the maximum height of the stone we could derivate h(t) and makes the derivative equals to 0.

`h^(\prime)(t)=-32t+156`
`-32t+156=0`
`-32t=-156`
`t=(-156)/(-32)=4.875`

The stone will reach its maximum height at t=4.875 seconds. The height is:

`h(4.875)=-16(4.875)^2+156(4.875)+20^{}`
`h(4.875)=400.25`

its maximum height is 400.25 ft