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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 time taken for the rocket to reach its maximum height is; 1.25 seconds.

The maximum height reached by the toy rocket is; 44.5 feet.

What is the maximum height reached by the rocket?

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 40t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 40 = 0

-32t = -40

t = -40/-32

t = 1.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 1.25 seconds.

Also, the maximum height reached by the rocket is at; h (1.25);

h(1.25) = -16(1.25)² + 40 (1.25) + 7

= -25 + 62.5 + 7

= 44.5

The maximum height reached is; 44.5 feet.

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