Question

An aeroplane has to go from A point a to another point B, 500 km away due 30 degree east of north. Wind blowing due north at a speed of 20m/s. The air speed of the plane is 150 m/s. Find the time taken by the plane to go from A to B.

Answer 1

The vector diagram for various velocities is shown.

Vector AC gives velocity of aero plane 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,

(150/sin 30 degree) = (20/sin theta).

Therefore, sin( theta)=(20/300)=(1/15). Then,

Theta=sin^-1(1/15)=3.8 degree.

Angle NAC=33.8 degree.

The pilot should head the plane in the direction 33.8 degree east of north.