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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
    because:

    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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