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Question

An aeroplane has to go from a point A to another Point B,500 km away due 30o East of north. A wind is blowing due north at a speed of 20 m/s. The air speed of the plane is 150 m/s. (a) Find the direction in which the

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Solution

The vector diagram for various velocities is shown.Vector AC gives velocity of aeroplane relative to quiet air.Vector CB gives velocity of wind(air) relative to ground.Vector AB gives velocity of plane relative to ground.Using law of sines for triangle,

150sin300=20sinθ.

Therefore,sin(θ)=20300=115. Then,

Theta=sin1115=3.80.

Angle NAC=33.80.The pilot should head the plane in the direction 33.80 east of north


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