| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2003 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Closest approach when exact intercept not possible |
| Difficulty | Standard +0.3 This is a standard M4 relative velocity problem requiring vector decomposition and optimization. Part (a) is straightforward geometric reasoning about velocity components. Part (b) involves minimizing drift distance using calculus or geometric insight, which is a common textbook exercise for this module. The 5-mark allocation and structured parts make it slightly easier than average. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation1.10e Position vectors: and displacement1.10h Vectors in kinematics: uniform acceleration in vector form |
2.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{47e1d96b-4582-4324-a946-66989a2c66fc-2_455_1084_1112_487}
\end{center}
\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.
\begin{enumerate}[label=(\alph*)]
\item 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,
\item find, in terms of $u$ and $v$, the ratio of $B C$ to the width of the river.\\
(5)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2003 Q2 [8]}}