At noon a motorboat \(P\) is 2 km north-west of another motorboat \(Q\). The motorboat \(P\) is moving due south at \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The motorboat \(Q\) is pursuing motorboat \(P\) at a speed of \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and sets a course in order to get as close to motorboat \(P\) as possible.
Find the course set by \(Q\), giving your answer as a bearing to the nearest degree.
Find the shortest distance between \(P\) and \(Q\).
Find the distance travelled by \(Q\) from its position at noon to the point of closest approach.