AQA M3 2012 June — Question 6

Exam BoardAQA
ModuleM3 (Mechanics 3)
Year2012
SessionJune
TopicVectors Introduction & 2D

6 At noon, two ships, \(A\) and \(B\), are a distance of 12 km apart, with \(B\) on a bearing of \(065 ^ { \circ }\) from \(A\). The ship \(B\) travels due north at a constant speed of \(10 \mathrm {~km} \mathrm {~h} ^ { - 1 }\). The ship \(A\) travels at a constant speed of \(18 \mathrm {~km} \mathrm {~h} ^ { - 1 }\).
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  1. Find the direction in which \(A\) should travel in order to intercept \(B\). Give your answer as a bearing.
  2. In fact, the ship \(A\) actually travels on a bearing of \(065 ^ { \circ }\).
    1. Find the distance between the ships when they are closest together.
    2. Find the time when the ships are closest together.