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Question

An airplane pilot wish to fly due west while wind is blowing towards south at 100 km/hr . If the speed of the airplane with respect to blowing wind is 200 km/hr, in which direction should the pilot head to reach the destination ?

A
60 South of West
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B
30 West of North
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C
30 North of West
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D
45 North of West
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Solution

The correct option is C 30 North of West

Velocity of wind w.r.t ground:
vWG=100 km/hr

Velocity of plane w.r.t wind:
vPW=200 km/hr

vPG is velocity of plane w.r.t ground

vPG=vPW+vWG

From vector triangle shown in figure, if plane has to move towards west direction, then it has to fly at angle θ with west so, that resultant velocity vPG is in west direction.

Thus, from vector triangle:

vPWsinθ=vWG

sinθ=vWGvPW=100200=12

θ=30 North of West, required heading direction for pilot.

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