A small aircraft for one person is used on a short horizontal flight. On its journey from A to B, the resultant velocity of the aircraft is 15 m s^{−1} in a direction 60° east of north and the wind velocity is 7.5 m s^{−1} due north.

a. Show that for the aircraft to travel from A to B it should be pointed due east.

b. After flying 5 km from A to B, the aircraft returns along the same path from B to A with a resultant velocity of 13.5 m s−1. Assuming that the time spent at B is negligible, calculate the average speed for the complete journey from A to B and back to A.