An airplane flying at 82km/hr at 30 degrees east of north encounters a 40km/hr wind due west. What is the speed of the plane relative to the ground?

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  1. Apparently the first velocity you mentioned is the air speed, since you are asking for the ground speed. The problem should have made that more lear.

    The velocity of the plane with respect to the ground is the vector sum of the wind speed and the velocity of the plane with respect to the air.

    Vgy = 82 cos30 = 71.0 km/h (north component)
    Vgx = 82 sin30 - 40 = 1.0 km/h (east component)
    resultant = 71.0 km/h, 0.8 degrees E of N

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