Question

A toy rocket is shot vertically into the air from a launching pad 6 feel above the ground with an initial velocity of 64 feet per second. The height h, in feet, of the rocket above the ground as t seconds after launch is given by the function h(t)=-16t^2+64t+6. How long will it take the rocket to reach its maximum height? What is the maximum height?

Answer 1

How long will it take the rocket to reach its maximum height?

• 2 seconds

What is the maximum height?

• 70 feet

Explanation:

h(t) = -16t² + 64t + 6

in order to determine the maximum height we must find the derivative:

h'(t) = 2 · -16t + 64 = -32t + 64

0 = -32t + 64

32t = 64

t = 64/32 = 2 seconds

just replace t by 2 in order to determine the maximum height:

maximum height = -16·2² + 64·2 + 6 = -64 + 128 + 6 = 70 feet