Question

The map below shows that Atlanta is 730 miles in a direction 5.00° north of east from Dallas, and that Chicago is 560 miles in a direction 21.0° west of north from Atlanta. Assuming the Earth may be approximated as flat across this map, what is the displacement from Dallas to Chicago? Find its magnitude (in mi) and direction (in degrees) as measured counterclockwise from due east of Dallas.

magnitude____________ mi

direction_____________ ° counterclockwise from due east of Dallas

Answer 1

X_COMPONENT of Dallas to Atlanta =730 cos (5°)

=727.2miles

X _component of Atlanta to Chicago = -560 cos(69°) = -200.68miles

Adding the both component =526.51miles

similarlly

Y_COMPONENT Of Dallas to Atlanta =730*Sin (5°)

=63.62miles

Y component of Atlanta to Chicago = 560*Sin(69°)= 522.8 miles

Adding the both Y component  =586.42 miles

now Using Pythagoras Theorem

Displacement of Dallas to Chicago is = √ ( 586.42² + 526.51²)

=788.10 miles

direction tan θ =586.42/526.51

=1.113

so angle θ =tan^-1(1.113)

=48.08 degree

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