\includegraphics{figure_4}
Mary swims in still water at 0.85 m s\(^{-1}\). She swims across a straight river which is 60 m wide and flowing at 0.4 m s\(^{-1}\). She sets off from a point \(A\) on the near bank and lands at a point \(B\), which is directly opposite \(A\) on the far bank, as shown in Fig. 4.
Find
- the angle between the near bank and the direction in which Mary swims,
[3]
- the time she takes to cross the river.
[3]
\includegraphics{figure_5}
A little further downstream a large tree has fallen from the far bank into the river. The river is modelled as flowing at 0.5 m s\(^{-1}\) for a width of 40 m from the near bank, and 0.2 m s\(^{-1}\) for the 20 m beyond this. Nassim swims at 0.85 m s\(^{-1}\) in still water. He swims across the river from a point \(C\) on the near bank. The point \(D\) on the far bank is directly opposite \(C\), as shown in Fig. 5. Nassim swims at the same angle to the near bank as Mary.
- Find the maximum distance, downstream from \(CD\), of Nassim during the crossing.
[5]
- Show that he will land at the point \(D\).
[4]