An aeroplane has to go from a point A to another point B, 500 km away due 30° cast 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 pilot should head the plane to reach the point B. (b) Find the time taken by the plane to go from A to B.

Given:
Distance between points A and B = 500 km
B from A is east of north.
Speed of wind due north, = 20 m/s
Airspeed of the plane, = 150 m/s
Let,

is the resultant direction of the plane to reach point B.

(a) Using the sine formula in ACB, we get:

⇒

⇒

Direction of the aeroplane is east of line AB.

(b) Time taken by the plane to reach point B from point A:

⇒ ’