| 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 | Minimum speed to intercept |
| Difficulty | Standard +0.8 This M4 relative velocity/interception problem requires vector analysis and optimization. Part (a) demands recognizing that minimum speed occurs when C's velocity is perpendicular to S's position vector, requiring trigonometric insight beyond routine application. Part (b) involves solving the interception triangle with given speed, requiring careful vector geometry and bearing calculations. The multi-step reasoning and non-standard setup elevate this above typical mechanics questions. |
| Spec | 3.02e Two-dimensional constant acceleration: with vectors |
A coastguard ship $C$ is due south of a ship $S$. Ship $S$ is moving at a constant speed of 12 km h$^{-1}$ on a bearing of 140°. Ship $C$ moves in a straight line with constant speed $V$ km h$^{-1}$ in order to intercept $S$.
\begin{enumerate}[label=(\alph*)]
\item Find, giving your answer to 3 significant figures, the minimum possible value for $V$.
[3]
\end{enumerate}
It is now given that $V = 14$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the bearing of the course that $C$ takes to intercept $S$.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2013 Q5 [8]}}