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physics

A spelunker is surveying a cave. She follows a passage 120 m straight west, then 210 m in a direction 45∘ east of south, and then 280 m at 30∘ east of north. After a fourth unmeasured displacement, she finds herself back where she started.

A. Use a scale drawing to determine the magnitude of the fourth displacement.

B. Determine the direction of the fourth displacement. (....) south of west

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  1. Unless otherwise stated, all angles are measured CCW from the
    +x-axis.

    D = -120 + 210[315o] + 280[60o].

    X = -120 + 210*Cos315 + 280*Cos60
    = 168.5 m.
    Y=210*sin315 + 280*sin60 = 94 m.

    Tan A = Y/X = 94/168.5 = 0.55786
    A = 29.2o

    D = X/Cos A = 168.5/Cos29.2 = 193 m[29o].

    b. Direction = 29 + 180 = 209o =
    29o S. of W.

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