An aeroplane has to go from a point A to another point B, 500 km away due 30∘ east of north. Wind is blowing due north at a speed of 20 m/s. The steering-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.