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Math Help - direction plane question

  1. #1
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    direction plane question

    The captain of a plane wishes to proceed due west. Now the cruising speed of the plane is 275 meters per seconds relative to the air. A weather report indicates that a 38.0 meter per second wind is blowing from the south to the north. In what direction, measured with respect to due west, should the pilot head the plane relative to the air?

    in degrees? north or south (of west)
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  2. #2
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    Quote Originally Posted by rcmango View Post
    The captain of a plane wishes to proceed due west. Now the cruising speed of the plane is 275 meters per seconds relative to the air. A weather report indicates that a 38.0 meter per second wind is blowing from the south to the north. In what direction, measured with respect to due west, should the pilot head the plane relative to the air?

    in degrees? north or south (of west)
    Too many relatives.

    In what direction, measured with respect to due west, should the pilot head the plane relative to the air?

    "relative to the air" means when there is no wind blowing?

    Anyway, if I understand what the Problem means,
    the figure is that of a right triangle, with these:
    ---vertical leg = velocity of wind = 38 m/sec
    ---horizonta leg = unknown
    ---hypotenuse = velocity of plane when no wind blowing = 275 m/sec
    ---angle between horizopntal leg and hypotenuse = alpha = direction of plane to due West.

    So,
    275sin(alpha) = 38
    sin(alpha) = 38/275
    alpha = arcsin(38/275)
    alpha = 7.94265 degrees

    Therefore, the plane should fly S 82.05735degrees W. --------------answer.
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