Edexcel M4 2003 June — Question 2

Exam BoardEdexcel
ModuleM4 (Mechanics 4)
Year2003
SessionJune
TopicVectors Introduction & 2D

2. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{47e1d96b-4582-4324-a946-66989a2c66fc-2_455_1084_1112_487}
\end{figure} A man, who rows at a speed \(v\) through still water, rows across a river which flows at a speed \(u\). The man sets off from the point \(A\) on one bank and wishes to land at the point \(B\) on the opposite bank, where \(A B\) is perpendicular to both banks, as shown in Fig. 1.
  1. Show that, for this to be possible, \(v > u\). Given that \(v < u\) and that he rows from \(A\) so as to reach a point \(C\), on the opposite bank, which is as close to \(B\) as possible,
  2. find, in terms of \(u\) and \(v\), the ratio of \(B C\) to the width of the river.
    (5)