   Chapter 3.9, Problem 19E ### 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

# A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking south at 5 ft/s from a point 500 fl due east of P. At what rate are the people moving apart 15 min after the woman starts walking?

To determine

To find: The rate at which the people moving apart 15 min after the women starts walking.

Explanation

Given:

A man starts walking towards North at 4 ft/s from a fixed point P.

After 5 minutes later a women starts walking towards South at 5 ft/s from a 500 ft due East of the fixed point P.

Formula used:

(1) Chain rule: dydx=dydududx

(2) Pythagorean Theorem for the Right angle triangle.

Calculation:

Let P be the fixed point and x is the distance travelled by man towards North, and z is the distance between the people and y is the distance travelled by the women from 500 ft due to the point P towards South as shown below in the Figure 1.

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

Hence x, y and z are the function of the time variable t .

Apply Pythagorean Theorem in the above triangle ABC,

z2=(x+y)2+5002

Obtain dzdt, 15 minutes after the woman starts walking.

After 15 minutes later the position of man from the point P:

x=velocity×time=4×20×60[Q1min=60s]=4,800ft

After 15 minutes later position of y from the point P:

y=velocity×time=6×15×60[Q1min=60s]=4,500ft

And distance between man and woman 15 minutes later:

z2=[(4,800+4,500)2+5002]=[9,3002+5002]=[86,490,000+250,000]=[86,740,000]

On further simplification the required distance between people.

z=86,740,000ft

Differentiate z 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

#### Find the median for the following set of scores: 1, 9, 3, 6, 4, 3, 11, 10

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### In Exercises 7-28, perform the indicated operations and simplify each expression. 16. x1x+2x+3x21

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

#### In Problems 19-44, factor completely. 41.

Mathematical Applications for the Management, Life, and Social Sciences

#### How does a full-text database differ from other databases?

Research Methods for the Behavioral Sciences (MindTap Course List) 