| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | River crossing: reach point directly opposite (find angle and/or time) |
| Difficulty | Standard +0.3 This is a standard M1 relative velocity problem requiring resolution of velocities and basic trigonometry. Students must set up perpendicular components (ferry velocity cancels river flow), solve V = 3/sin(60°), then find crossing time using distance/perpendicular component. Straightforward application of a well-practiced technique with no novel insight required, making it slightly easier than average. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication |
4 A small ferry is used to cross a river which has straight parallel banks that are 200 metres apart. The water in the river moves at a constant speed of $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The ferry travels from a point $A$ on one bank to a point $B$ directly opposite $A$ on the other bank. The velocity of the ferry relative to the water is $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $60 ^ { \circ }$ to the upstream bank, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{d42b2e88-74ea-486b-bb47-f512eb0c185d-4_467_1122_550_459}
\begin{enumerate}[label=(\alph*)]
\item $\quad$ Find $V$.
\item Find the time that it takes for the ferry to cross the river, giving your answer to the nearest second.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2012 Q4 [6]}}