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A truck driver travels a distance of 100 miles due East. He then turns at an angle of 35 degrees S of E and travels a distance of 50 miles.

What is the resultant displacement?
What is the direction?

  • physics! -

    Just add the two vectors.

    The eastward displacement is
    X = 100 + 50 cos35 = 140.96 miles

    The northern displacement (assuming north is positive) is
    Y = -50 sin35 = -28.68 miles
    (The minus sign is there because the second vector is south of east, not north).

    Total displacementis
    = sqrt[(140.96)^2 + (-28.68)^2]

    The direction(measured south of east) is tan^-1 (28.68/140.96) = 11.5 degrees

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