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A plane is flying at 25 degrees north of west at 190km/ h. Suddenly there is a wind from 15degrees north of east at 45 km/ hr. what is the planes new velocity with respect to ground in standard position

  • Physics -

    V = 190km/h @ 155o + 45km/h @ 15o.

    X = 190*cos155 + 45*cos15=-128.73 km/h.
    Y = 190*sin155 + 45*sin15=91.94 km/h.

    tanAr = Y/X = 91.94/-128.73 = 0.71424
    Ar = -35.53o = Reference angle.
    A = -35.54 + 180 = 144.5o

    V = X/cosA = -128.73/cos144.5=158.1 km/h
    @ 144.5o, CCW.

    Note: One student said that the book's
    answer is 227 km/h @ 162.4o. Based on
    the INFO given, that would be impossible

    1. The direction of the wind reduces
    the speed of the plane.

    2. The resultant direction would have to be less than 155o.

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