- \hspace{0pt} [In this question the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are due east and due north respectively.]
A coastguard station \(O\) monitors the movements of a small boat.
At 10:00 the boat is at the point \(( 4 \mathbf { i } - 2 \mathbf { j } ) \mathrm { km }\) relative to \(O\).
At 12:45 the boat is at the point \(( - 3 \mathbf { i } - 5 \mathbf { j } ) \mathrm { km }\) relative to \(O\).
The motion of the boat is modelled as that of a particle moving in a straight line at constant speed.
- Calculate the bearing on which the boat is moving, giving your answer in degrees to one decimal place.
- Calculate the speed of the boat, giving your answer in \(\mathrm { kmh } ^ { - 1 }\)