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!

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 at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

Time to reach the maximum height

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

The maximum height

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

Read more about height functions at

https://brainly.com/question/10837575

#SPJ1

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada