   Chapter 1, Problem 68P

Chapter
Section
Textbook Problem

A map suggests that Atlanta is 730. miles in a direction 5.00° north of east from Dallas. The same map shows that Chicago is 560. miles in a direction 21.0° west of north from Atlanta. Figure P1.68 shows the location of these three cities. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago. Figure P1.68

To determine
The displacement from the Dallas to Chicago.

Explanation

Given Info: The location of Atlanta is at a direction 5° north of east from Dallas. The location of Chicago is at a direction 21° west of north from Atlanta.

Explanation:

The vector representation of the location is given below,

The x component of the displacement is,

x=[(730mile)cos(5°)][(560mile)cos(21°)]=527mile

The y component of the displacement is,

y=[(730mile)cos(5°)]+[(560mile)sin(21°)]=586mile

Formula to calculate the resultant displacement from Dallas to Chicago is,

R=x2+y2

• R is resultant displacement,
• xandy are the component of the displacement,

Substitute 527mile for x , 586mile for y to find R

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