| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Relative velocity: find resultant velocity (magnitude and/or direction) |
| Difficulty | Moderate -0.3 This is a standard M1 relative velocity question requiring vector addition with given bearing information. Part (a) involves straightforward trigonometry (sin 30° = 0.5) to find the wind speed, and part (b) requires calculating the resultant magnitude using Pythagoras. The setup is clear, the mathematics is routine, and it's a typical textbook exercise slightly easier than average A-level difficulty. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.10d Vector operations: addition and scalar multiplication1.10h Vectors in kinematics: uniform acceleration in vector form |
| Answer | Marks | Guidance |
|---|---|---|
| \(V = 150 \tan 30° = 86.6 \text{ ms}^{-1}\) | M1 | Using trigonometry (usually tan or sine rule) to find \(V\) |
| A1 | AG Correct answer from correct working. (Division by 2 only acceptable if sin30° or cos60° seen) | |
| OR | ||
| \(\frac{V}{\sin 30°} = \frac{150}{\sin 60°}\) AG \(V = 86.6 \text{ ms}^{-1}\) | ||
| Total: 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{150}{v} = \cos 30°\) | M1 | Using trigonometry or Pythagoras to find \(v\) |
| \(v = \frac{150}{\cos 30°} = 173 \text{ ms}^{-1} \text{ (to 3sf)}\) | A1 | Correct expression |
| A1 | Correct answer | |
| Total: 3 marks |
**5(a)**
| $V = 150 \tan 30° = 86.6 \text{ ms}^{-1}$ | M1 | Using trigonometry (usually tan or sine rule) to find $V$ |
| | A1 | AG Correct answer from correct working. (Division by 2 only acceptable if sin30° or cos60° seen) |
| **OR** | | |
| $\frac{V}{\sin 30°} = \frac{150}{\sin 60°}$ AG $V = 86.6 \text{ ms}^{-1}$ | | |
| **Total: 2 marks** | | |
**5(b)**
| $\frac{150}{v} = \cos 30°$ | M1 | Using trigonometry or Pythagoras to find $v$ |
| $v = \frac{150}{\cos 30°} = 173 \text{ ms}^{-1} \text{ (to 3sf)}$ | A1 | Correct expression |
| | A1 | Correct answer |
| **Total: 3 marks** | | |5 An aeroplane flies in air that is moving due east at a speed of $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The velocity of the aeroplane relative to the air is $150 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ due north. The aeroplane actually travels on a bearing of $030 ^ { \circ }$.
\begin{enumerate}[label=(\alph*)]
\item Show that $V = 86.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, correct to three significant figures.
\item Find the magnitude of the resultant velocity of the aeroplane.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2007 Q5 [5]}}