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March 24, 2017

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The pilot of an aircraft wishes to fly due west in a 46.8 km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 204 km/h.
(a) In what direction should the aircraft head?
° north of west
(b) What should its speed relative to the ground be?
km/h

  • physics - ,

    a. X = -204 km/h.
    Y = -46.8 km/h.

    tanA = Y/X = -46.8/-204 = 0.22941.
    Ar = 12.9o South of West.

    The plane should head 12.9o North of West.

    b. A = 180 + Ar = 180 + 12.9 = 192.9o
    V = X/cosA = -204/cos192 = 209.3 km/h.

  • physics - ,

    a. Vpa = Vpg + Va = -204 km/h
    Vpg - 46.8i = -204
    Vpg = -204 + 46.8i

    Tan Ar = Y/X = 46.8/-204 = -0.22941
    Ar = -12.9o = Reference angle.
    A = -12.9 + 180 = 167.1o CCW = 12.9o N.
    of W. = Direction.

    b. Vpg = X/Cos A = -204/Cos167.1 = 209.3 m/s. = Velocity of plane relative to gnd.

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