| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2014 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Interception: find bearing/direction to intercept (exact intercept) |
| Difficulty | Challenging +1.2 This is a standard M4 interception problem requiring vector resolution and solving a quadratic equation for minimum time. While it involves multiple steps (setting up position vectors, minimizing distance/time, finding bearing), the method is well-practiced in M4 and follows a predictable template. The calculation is moderately involved but conceptually straightforward for students who have studied relative velocity and interception, placing it above average difficulty but not requiring novel insight. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form |
At noon two ships $A$ and $B$ are 20 km apart with $A$ on a bearing of 230° from $B$. Ship $B$ is moving at 6 km h$^{-1}$ on a bearing of 015°. The maximum speed of $A$ is 12 km h$^{-1}$. Ship $A$ sets a course to intercept $B$ as soon as possible.
\begin{enumerate}[label=(\alph*)]
\item Find the course set by $A$, giving your answer as a bearing to the nearest degree. [4]
\item Find the time at which $A$ intercepts $B$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2014 Q4 [8]}}