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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 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 at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

What is the maximum height the rocket reached?

Given function:

h(t) = -16t² + 72t + 7

By differentiating the function, we have

h'(t) = -32t + 72

Set the function to 0

-32t + 72 = 0

32t = 72

Divide both sides by 32

t = 2.25

Hence, the time is 2.25 seconds

To find the maximum height reached by the rocket,

Substitute t = 2.25 into

h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

= -16(5.0625) + 162 + 7

= -81 + 162 + 7

h(2.25) = 88

In conclusion, the maximum height the rocket reached is 88 feet

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