The compass of an airplane indicates that it is headed due north, and its airspeed indicator shows that it is moving through the air at 240 km/hr. If there is a wind of 100 km/hr from west to east, what is the velocity of the airplane?
Answer
A
155 km/hr with directional bearing N65.8˚E
B
260 km/hr with directional bearing N67.4˚E
C
260 km/hr with directional bearing N22.6˚E
D
155 km/hr with directional bearing N24.6˚E
Explanation
The airplane’s velocity relative to the ground combines its 240 km/hr northward airspeed with the 100 km/hr eastward wind. Its speed is √(240² + 100²) = 260 km/hr. The direction east of north is arctan(100/240) ≈ 22.6°, so the velocity is 260 km/hr with bearing N22.6°E, choice C.
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