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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 40 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16t²+40t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?

The rocket reaches its maximum height at 1.25 second(s) after launch. (Simplify your answer.)

The maximum height reached by the object is _____ feet. (Simplify your answer.)

A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 40 feet

Answer :

The rocket reaches its maximum height at 1.25 second(s) after launch

The maximum height reached by the object is 32 feet.

Time to reach the maximum height

The function is given as

h(t) = -16t² + 40t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 40

Set to 0

-32t + 40 = 0

So, we have

32t = 40

Divide by 32

t = 1.25

Hence, the time is 1.25 seconds

The maximum height

In (a), we have

t = 1.25

Substitute t = 1.25 in h(t) = -16t² + 40t + 7

h(1.25) = -16(1.25)² + 40(1.25) + 7

Evaluate

h(1.25) = 32

Hence, the maximum height is 32 feet

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