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24 August, 18:43

The pilot of an airplane notes that the compass indicates heading west. The airplane's speed relative to the air is 100 km/h. The air is moving in a wind at 25.0 km/h toward the north. Find the velocity, magnitude and direction of the airplane relative to the ground.

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  1. 24 August, 18:49
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    The airplane's speed relative to the ground is

    √ (100² + 25²)

    = √ (10,000 + 625)

    = √ 10,625

    = 103.08 km/hr.

    The angle of its velocity north of west is

    the angle whose tangent is (25/100)

    arctan (25/100) = 14° north of west.

    (bearing = 284°)
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