   Chapter 4.1, Problem 63E

Chapter
Section
Textbook Problem

Lunar Gravity On the moon, the acceleration of a free-falling object is a ( t ) = − 1.6 meters per second per second. A stone is dropped from a cliff on the moon and hits the surface of the moon 20 seconds later. How far did it fall? What was its velocity at impact?

To determine

To calculate: The height of falling of stone and velocity at impact if acceleration of free falling object is a(t)=1.6 meter per sec per sec.

Explanation

Given:

On the moon, the acceleration of free falling object is a(t)=1.6 meter per sec per sec. The time taken by the stone to hit the ground is 20 sec.

Formula used:

Integration, xndx=xn+1n+1+C.

Calculation:

Let t=0 represent the initial time and the position of the stone is y at any instant. The time taken by the stone to hit the ground is,

t=20 sec

The initial velocity of stone is 0 meter per second. So,

y(0)=0

Since, the acceleration due to gravity g=1.6 meter per second per second. So, the equation is written as,

y=1.6

Integrate the above equation with respect to t,

y=1.6dt=1.6t+C1

Let the initial velocity of the object is y(0)=0. Now, find the value of C1,

y(0)=1.6(0)+C10=C1

Now, the equation y is written as,

y=1.6t …...…... (1)

Again, integrate the above equation,

y=(1

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Rationalize Numerator Rationalize the numerator. 91. 153

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 19-24, find the functions f + g, f g, fg, and fg. 22. f(x) =1x2+1; g(x) = 1x21

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Find all prime ideals of .

Elements Of Modern Algebra

True or False: If f′(c) = 0 and f″(c) < 0, then c is a local minimum.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 