11 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 \( 15 \mathrm{~ms}^{-1} \) in a direction \( 60^{\circ} \) cast of north and the wind velocity is \( 7.5 \mathrm{~ms}^{-1} \) due north.
Figure 1.20
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 \( 13.5 \mathrm{~m} \mathrm{~s}^{-1} \). 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 .