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. The figure below shows the location of these three cities. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

I got 621 miles & 70.8 N of E.

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  1. Convention:
    XY : Cartesian Displacement Vector from X to Y.

    Using appropriate capitals for the cities, and the unit vectors î and ĵ for direct East and North.

    Dalas to Atlanta is 730 miles 5.00° N of E:
    DA = 730 [cos(5.00°) î + sin(5.00°) ĵ]

    Atlanta to Chicago 560 miles 21.0° W of N:
    AC = 560 [-sin(21.0°) î + cos(21.0°) ĵ]

    So from Dalas to Chicago is then:
    DC = DA + AC

    DC = [(730 cos(5.00°)-560 sin(21.0°)) î + (730 sin(5.00°) + 560 cos(21.0°)) ĵ]

    DC ≈ [526.5 î + 586.4 ĵ]

    DC ≈ 788.1 [cos(48.08°) î + sin(48.08°) ĵ]

    That is, 788.1 miles 48.08° North of East.

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  2. 77738

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  3. Oh wow I thought you where who was talking trash about kids cheating UwU

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