A map suggests that Atlanta is d 1 = 729 mi in a direction of 1 = 4.98° north of

Question

A map suggests that Atlanta is d1 = 729 mi in a direction of 1 = 4.98° north of east from Dallas. The same map shows that Chicago is d2 = 560 miles in a direction of 2 = 21.2° west of north from Atlanta. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

magnitude   ------ . mi direction --------- ° north of east of Dallas
A map suggests that Atlanta is di 729 mi in a direction of 01 4.98° north of east from Dallas. The same map shows that Chicago is d2 560 miles in a direction of 62 21.2° west of north from Atlanta. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago. magnitude direction Your response differs from the correct answer by more than 10%. Double check your calculations. mi north of east of Dallas Chicago di Atlanta Dallas Need Help? Read It

Explanation / Answer

Solution,

Horizontal component of 1st vector, = 729 cos4.98 = 726.25 miles

Horizontal component of the 2nd vector = -560 cos68.8 = - 202.51 miles

Summation of horizontal component = 523.74 miles

similarly

Vertical component of 1st vector,= 729 sin4.98 = 63.28 miles

Vertical component of 2nd vector = 560 sin68.8 = 522.10 miles

Summation of vertical component = 585.38 miles

Now the net displacement from Dallas to Chicago = sqrt(523.74^2 + 585.38^2) = 785.48 miles

Direction, theta =arctan (585.38/523.74) = 48.18 degree

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