| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2002 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Minimum speed to intercept |
| Difficulty | Challenging +1.2 This is a mechanics interception problem requiring vector resolution, relative velocity concepts, and optimization (minimizing speed/time). While it involves multiple steps and geometric reasoning about bearings and velocities, the techniques are standard for M4 level—setting up position vectors, using perpendicularity for minimum speed, and solving a quadratic for interception time. More challenging than routine C1-C3 questions but typical for Further Maths mechanics. |
| 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. Ship $A$ is steaming on a bearing of $060 ^ { \circ }$ at $30 \mathrm {~km} \mathrm {~h} ^ { - 1 }$ and at 9 a.m. it is 20 km due west of a second ship $B$. Ship $B$ steams in a straight line.
\begin{enumerate}[label=(\alph*)]
\item Find the least speed of $B$ if it is to intercept $A$.
Given that the speed of $B$ is $24 \mathrm {~km} \mathrm {~h} ^ { - 1 }$,
\item find the earliest time at which it can intercept $A$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2002 Q2 [10]}}