3 A fishing boat is travelling between two ports, \(A\) and \(B\), on the shore of a lake. The bearing of \(B\) from \(A\) is \(130 ^ { \circ }\). The fishing boat leaves \(A\) and travels directly towards \(B\) with speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). A patrol boat on the lake is travelling with speed \(4 \mathrm {~ms} ^ { - 1 }\) on a bearing of \(040 ^ { \circ }\).
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1. Find the velocity of the fishing boat relative to the patrol boat, giving your answer as a speed together with a bearing.
2. When the patrol boat is 1500 m due west of the fishing boat, it changes direction in order to intercept the fishing boat in the shortest possible time.
   1. Find the bearing on which the patrol boat should travel in order to intercept the fishing boat.
   2. Given that the patrol boat intercepts the fishing boat before it reaches \(B\), find the time, in seconds, that it takes the patrol boat to intercept the fishing boat after changing direction.
   3. State a modelling assumption necessary for answering this question, other than the boats being particles.