| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | River crossing: perpendicular heading or minimum time (find drift and/or time) |
| Difficulty | Standard +0.3 This is a standard M4 relative velocity river-crossing problem with straightforward application of vector methods. Part (a) requires recognizing that minimum time means swimming perpendicular to banks; part (b) is simple drift calculation; part (c) involves resolving velocities to swim directly to B. All are textbook exercises requiring routine application of learned techniques with no novel insight, making it slightly easier than average. |
| Spec | 3.02e Two-dimensional constant acceleration: with vectors |
\includegraphics{figure_1}
A river is 50 m wide and flows between two straight parallel banks. The river flows with a uniform speed of $\frac{2}{3}$ m s$^{-1}$ parallel to the banks. The points $A$ and $B$ are on opposite banks of the river and $AB$ is perpendicular to both banks of the river, as shown in Figure 1.
Keith and Ian decide to swim across the river. The speed relative to the water of both swimmers is $\frac{10}{9}$ m s$^{-1}$.
Keith sets out from $A$ and crosses the river in the least possible time, reaching the opposite bank at the point $C$. Find
\begin{enumerate}[label=(\alph*)]
\item the time taken by Keith to reach $C$,
[2]
\item the distance $BC$.
[2]
\end{enumerate}
Ian sets out from $A$ and swims in a straight line so as to land on the opposite bank at $B$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the time taken by Ian to reach $B$.
[4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2013 Q2 [8]}}