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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 ___ second(s) after launch.

(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 2.25 second(s) after launch

The maximum height reached by the rocket is 88 feet.

What is the maximum height the rocket reached?

Given function:

h(t) = -16t² + 40t + 7

By differentiating the function, we have

h'(t) = -32t + 40

Set the function to 0

-32t + 40 = 0

32t = 40

Divide both sides by 32

t = 1.25

Hence, the time is 1.25 seconds

To find the maximum height reached by the rocket,

Substitute t = 1.25 into

h(t) = -16t² + 40t + 7

h(1.25) = -16(1.25)² + 40(1.25) + 7

= -16(1.5625) + 162 + 7

= -25 + 50 + 7

h(1.25) = 32

In conclusion, the maximum height the rocket reached is 32 feet

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