| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | June |
| Marks | 10 |
| 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 M1 relative velocity problem with river crossing. It requires resolving velocities into components, using time = distance/speed, and applying the velocity triangle relationship. The multi-part structure and geometric setup are typical for mechanics questions, but the methods are straightforward applications of taught techniques with no novel insight required. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication |
I appreciate you providing the template, but I notice that no actual mark scheme content was included in your message. You've provided the instruction format and labeled it "Question 4:" followed by just "4", but there's no extracted mark scheme text to clean up.
Could you please provide the actual mark scheme content you'd like me to clean? Once you share the text with the unicode symbols and marking annotations, I'll convert it to LaTeX notation and format it properly.4 A boat is crossing a river, which has two parallel banks. The width of the river is 20 metres. The water in the river is flowing at a speed of $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The boat sets off from the point $O$ on one bank. The point $A$ is directly opposite $O$ on the other bank. The velocity of the boat relative to the water is $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $70 ^ { \circ }$ to the bank. The boat lands at the point $B$ which is 3 metres from $A$. The angle between the actual path of the boat and the bank is $\alpha ^ { \circ }$. The river and the velocities are shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{788534a5-abbb-4d6a-87b2-c54e859a128a-10_490_1307_641_370}
\begin{enumerate}[label=(\alph*)]
\item Find the time that it takes for the boat to cross the river.
\item Find $\alpha$.
\item $\quad$ Find $V$.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2014 Q4 [10]}}