Given:

Height of the rocket as a function of time

h(t) = -8t^2 +288t + 40

Find:

a) time for it to reach max height

b) max height

Solution:

a)

The rocket reaches maximum height when the velocity is zero

To find the velocity function we take the derivative of the height function

V(t) = -16t+288

We now set the function equal to zero

0 = -16t+288

t = 18 seconds

Maximum velocity is achieved at this time

b) What is the maximum height ?

Using the time from part (a)

We plug this time into our height function

h(18) = -8 * (18)^2 + 288 * (18) + 40

h(18) = 2632 ft