| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Interception: verify/find meeting point (position vector method) |
| Difficulty | Moderate -0.3 This is a standard M1 kinematics question using vector notation. Part (a) is routine application of r = r₀ + vt. Parts (b) and (c) require equating position vectors and solving simultaneous equations, which is a common textbook exercise. The multi-step nature and 11 marks elevate it slightly above trivial, but it requires no novel insight—just methodical application of standard techniques. |
| Spec | 1.10d Vector operations: addition and scalar multiplication1.10h Vectors in kinematics: uniform acceleration in vector form |
[In this question $\mathbf{i}$ and $\mathbf{j}$ are horizontal unit vectors due east and due north respectively. Position vectors are given with respect to a fixed origin $O$.]
A ship $S$ is moving with constant velocity $(3\mathbf{i} + 3\mathbf{j})$ km h$^{-1}$. At time $t = 0$, the position vector of $S$ is $(-4\mathbf{i} + 2\mathbf{j})$ km.
\begin{enumerate}[label=(\alph*)]
\item Find the position vector of $S$ at time $t$ hours. [2]
\end{enumerate}
A ship $T$ is moving with constant velocity $(-2\mathbf{i} + n\mathbf{j})$ km h$^{-1}$. At time $t = 0$, the position vector of $T$ is $(6\mathbf{i} + \mathbf{j})$ km. The two ships meet at the point $P$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the value of $n$. [5]
\item Find the distance $OP$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2013 Q6 [11]}}