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.)

Question

College

We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Answer :

adioabiola adioabiola · Answer 1 · 2024-02-14T11:53:29-05:00

The time taken for the rocket to reach its maximum height is; 2.25 seconds.

The maximum height reached by the toy rocket as evaluated from the given parameters is; 88 feet.

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 + 72t + 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 + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.