| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Angle change from impulse |
| Difficulty | Standard +0.3 This is a straightforward M2 impulse-momentum question requiring standard vector calculations: applying impulse-momentum theorem to find final velocity, calculating speeds using Pythagoras, and finding angle between vectors using dot product or component methods. All steps are routine applications of learned techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.03c Momentum in 2D: vector form6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \((-6\mathbf{i} + 8\mathbf{j}) = 0.2\left[\mathbf{v} - (20\mathbf{i} - 16\mathbf{j})\right]\) | M1 | Impulse momentum equation. Condone subtraction in wrong order |
| A1 | Correctly substituted equation | |
| \(\mathbf{v} = (-10\mathbf{i} + 24\mathbf{j})\) | A1 | |
| \( | \mathbf{v} | = \sqrt{(-10)^2 + 24^2}\) |
| \(= 26\ \text{ms}^{-1}\) | A1 | From cwo |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\tan\alpha = \frac{16}{20},\quad \tan\beta = \frac{24}{10}\) | M1 | Use trig to find two relevant angles |
| \(\alpha = 38.7°,\quad \beta = 67.4°\quad (51.3°, 22.6°)\) | A1ft | Both correct — seen or implied. Follow their \(\mathbf{v}\) |
| DM1 | Dependent on previous M1. Combine correctly to find required angle e.g. \(90° + 38.7° + 22.6°\) | |
| Angle is \(151°\) or \(209°\) | A1 | Accept \(151.3°\) or \(208.7°\) (2.635 or 3.648 radians) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Correct triangle | M1 | |
| \(\cos\theta = \frac{676 + 656 - 2500}{2\times 26\times\sqrt{656}}\) | DM1 | Award marks in order on epen |
| A1ft | Correct unsimplified. Follow their \(\mathbf{v}\) | |
| \(\theta = 151°\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Correct triangle | M1 | |
| \(\cos\theta = \frac{-200 - 384}{26\times\sqrt{656}}\) | DM1 | Award marks in order on epen |
| A1ft | Correct unsimplified. Follow their \(\mathbf{v}\) | |
| \(\theta = 151°\) | A1 |
# Question 4:
## Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $(-6\mathbf{i} + 8\mathbf{j}) = 0.2\left[\mathbf{v} - (20\mathbf{i} - 16\mathbf{j})\right]$ | M1 | Impulse momentum equation. Condone subtraction in wrong order |
| | A1 | Correctly substituted equation |
| $\mathbf{v} = (-10\mathbf{i} + 24\mathbf{j})$ | A1 | |
| $|\mathbf{v}| = \sqrt{(-10)^2 + 24^2}$ | M1 | Correct use of Pythagoras |
| $= 26\ \text{ms}^{-1}$ | A1 | From cwo |
## Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\tan\alpha = \frac{16}{20},\quad \tan\beta = \frac{24}{10}$ | M1 | Use trig to find two relevant angles |
| $\alpha = 38.7°,\quad \beta = 67.4°\quad (51.3°, 22.6°)$ | A1ft | Both correct — seen or implied. Follow their $\mathbf{v}$ |
| | DM1 | Dependent on previous M1. Combine correctly to find required angle e.g. $90° + 38.7° + 22.6°$ |
| Angle is $151°$ or $209°$ | A1 | Accept $151.3°$ or $208.7°$ (2.635 or 3.648 radians) |
### Alt(b) — Cosine rule method
| Answer/Working | Mark | Guidance |
|---|---|---|
| Correct triangle | M1 | |
| $\cos\theta = \frac{676 + 656 - 2500}{2\times 26\times\sqrt{656}}$ | DM1 | Award marks in order on epen |
| | A1ft | Correct unsimplified. Follow their $\mathbf{v}$ |
| $\theta = 151°$ | A1 | |
### Alt(b) — Scalar product method
| Answer/Working | Mark | Guidance |
|---|---|---|
| Correct triangle | M1 | |
| $\cos\theta = \frac{-200 - 384}{26\times\sqrt{656}}$ | DM1 | Award marks in order on epen |
| | A1ft | Correct unsimplified. Follow their $\mathbf{v}$ |
| $\theta = 151°$ | A1 | |
---4. A particle $P$ of mass 0.2 kg is moving with velocity $( 20 \mathbf { i } - 16 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ when it receives an impulse ( $- 6 \mathbf { i } + 8 \mathbf { j }$ ) N s.
\begin{enumerate}[label=(\alph*)]
\item Find the speed of $P$ immediately after it receives the impulse.\\
(5)
\item Find the size of the angle between the direction of motion of $P$ before the impulse is received and the direction of motion of $P$ after the impulse is received.\\
(4)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2017 Q4 [9]}}