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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 72 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)=-16 t²+72 t+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 ? 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 72 feet

Answer :

The rocket reaches its maximum height of 88 feet at 2.25 seconds after launch

How to find the time and the maximum height

The time

The function is given as

h(t) = -16t² + 72t + 7

To start with, we need to differentiate the function

h'(t) = -32t + 72

Next, we set the differentiated function to 0

-32t + 72 = 0

Next, we solve for the variable t

t = 2.25

This means that the time is 2.25 seconds

The maximum height

Recall that we have the value of t to be:

t = 2.25

Also, we have the equation to be

h(t) = -16t² + 72t + 7

So, we have

h(2.25) = -16(2.25)² + 72(2.25) + 7

Solve the expressions

h(2.25) = 88

This also means that the maximum height is 88 feet

Read more about height functions at

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