6 Two ships \(P\) and \(Q\) are moving on straight courses with constant speeds. At one instant \(Q\) is 80 km from \(P\) on a bearing of \(220 ^ { \circ }\). Three hours later, \(Q\) is 36 km due south of \(P\).
- Show that the velocity of \(Q\) relative to \(P\) is \(19.1 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) in the direction with bearing \(063.8 ^ { \circ }\) (both correct to 3 significant figures).
- Find the shortest distance between the two ships in the subsequent motion.
Given that the speed of \(P\) is \(28 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) and \(Q\) is travelling in the direction with bearing \(105 ^ { \circ }\), find
- the bearing of the direction in which \(P\) is travelling,
- the speed of \(Q\).