AQA M1 2012 January — Question 4

Exam BoardAQA
ModuleM1 (Mechanics 1)
Year2012
SessionJanuary
TopicVectors Introduction & 2D

4 A small ferry is used to cross a river which has straight parallel banks that are 200 metres apart. The water in the river moves at a constant speed of \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The ferry travels from a point \(A\) on one bank to a point \(B\) directly opposite \(A\) on the other bank. The velocity of the ferry relative to the water is \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(60 ^ { \circ }\) to the upstream bank, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{d42b2e88-74ea-486b-bb47-f512eb0c185d-4_467_1122_550_459}
  1. \(\quad\) Find \(V\).
  2. Find the time that it takes for the ferry to cross the river, giving your answer to the nearest second.