| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2008 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Bearing and speed from velocity vector |
| Difficulty | Standard +0.3 This is a standard relative velocity question requiring subtraction of velocity vectors, finding the angle using arctan, and converting to a bearing. It involves routine mechanics techniques with straightforward arithmetic, making it slightly easier than average for A-level mechanics. |
| Spec | 1.05a Sine, cosine, tangent: definitions for all arguments1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Notes |
| \(_Q\mathbf{V}_P = \mathbf{V}_Q - \mathbf{V}_P = (3\mathbf{i}+7\mathbf{j})-(5\mathbf{i}-4\mathbf{j})\) | M1 | |
| \(= (-2\mathbf{i}+11\mathbf{j})\) | A1 | |
| \(\tan\theta = \frac{11}{2} \Rightarrow \theta = 79.69°...\) | M1 A1 | |
| Bearing is \(350°\) | A1 | Total: 5 |
## Question 1:
| Working/Answer | Marks | Notes |
|---|---|---|
| $_Q\mathbf{V}_P = \mathbf{V}_Q - \mathbf{V}_P = (3\mathbf{i}+7\mathbf{j})-(5\mathbf{i}-4\mathbf{j})$ | M1 | |
| $= (-2\mathbf{i}+11\mathbf{j})$ | A1 | |
| $\tan\theta = \frac{11}{2} \Rightarrow \theta = 79.69°...$ | M1 A1 | |
| Bearing is $350°$ | A1 | **Total: 5** |
---\begin{enumerate}
\item \hspace{0pt} [In this question $\mathbf { i }$ and $\mathbf { j }$ are unit vectors due east and due north respectively.]
\end{enumerate}
A ship $P$ is moving with velocity ( $5 \mathbf { i } - 4 \mathbf { j }$ ) $\mathrm { km } \mathrm { h } ^ { - 1 }$ and a ship $Q$ is moving with velocity $( 3 \mathbf { i } + 7 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }$.
Find the direction that ship $Q$ appears to be moving in, to an observer on ship $P$, giving your answer as a bearing.\\
\hfill \mbox{\textit{Edexcel M4 2008 Q1 [5]}}