   Chapter 3.9, Problem 17E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Two cars start moving from the same point. One travels south at60 mi/h and the other travels west at 25 mi/h. At what rate is the distance between the cars increasing two hours later?

To determine

To find: At what rate the distance between the cars increasing two hours later.

Explanation

Given:

Two cars start moving from the same point.

One car travel towards South at 60 mi/h and another travel towards West at 25 mi/h.

That is, dxdt=60mi/h and dydt=25mi/h.

Formula used:

Pythagorean Theorem

Calculation:

Let x is the distance travelled by first car toward West and reach to the point C and y is the distance travelled by second car toward South and reach to the point B as shown in the Figure 1 given below.

The position of both cars is shown in the given below Figure-1 after two hours later.

Let z be the distance between the cars after two hours later as shown the above figure-1.

Then by using the Pythagorean Theorem

z2=x2+y2

Since x and y both changes with the time t, z also changes with time.

Obtain the position of cars two hours later:

Distance travelled by the first car toward West direction is

x=2(60)=120

Distance travelled by the second car toward South direction is:

y=2(25)=50

Therefore, distance between the both cars two hours later is

z=(120)2+(50)2=14,400+2,500=16,900=130

Differentiate z2=x2+y2 with respect to the time t

### 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

#### In problems 23-58, perform the indicated operations and simplify. 51.

Mathematical Applications for the Management, Life, and Social Sciences

#### . ∞ −∞ 1 −1

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

#### The area of the region at the right is:

Study Guide for Stewart's Multivariable Calculus, 8th 