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.

Question

Physics

Madeleine Buchanan

4 October, 00:28

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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Answers (1)

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Justine Avila · Answer 1

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°)