| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2011 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Sphere rebounds off fixed wall obliquely |
| Difficulty | Standard +0.3 This is a standard M4 mechanics problem involving coefficient of restitution and geometric reasoning with wall collisions. Students need to set up coordinates, apply the restitution formula (velocity component perpendicular to wall is reversed and multiplied by e=3/4, parallel component unchanged), and use similar triangles or trigonometry to find CX. While it requires careful setup and multiple steps, it follows a well-practiced template for two-wall collision problems with no novel insight required. |
| Spec | 6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| At \(X\): \(u\sin\alpha = v\sin\beta\) | M1A1 | |
| \(v\cos\beta = eu\cos\alpha\), so \(4v\cos\beta = 3u\cos\alpha\) | M1A1 | |
| Eliminate \(u\) and \(v\) by dividing: \(\dfrac{\tan\alpha}{3} = \dfrac{\tan\beta}{4}\) | M1 | |
| Substitute trig ratios: \(\dfrac{5-x}{3 \times 4} = \dfrac{x}{4 \times 7.5}\) | DM1A1 | |
| Solve for \(x\): \(37.5 - 7.5x = 3x\) | DM1 | |
| \(x = 3.57\) (m) or \(\dfrac{25}{7}\) | A1 |
# Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| At $X$: $u\sin\alpha = v\sin\beta$ | M1A1 | |
| $v\cos\beta = eu\cos\alpha$, so $4v\cos\beta = 3u\cos\alpha$ | M1A1 | |
| Eliminate $u$ and $v$ by dividing: $\dfrac{\tan\alpha}{3} = \dfrac{\tan\beta}{4}$ | M1 | |
| Substitute trig ratios: $\dfrac{5-x}{3 \times 4} = \dfrac{x}{4 \times 7.5}$ | DM1A1 | |
| Solve for $x$: $37.5 - 7.5x = 3x$ | DM1 | |
| $x = 3.57$ (m) or $\dfrac{25}{7}$ | A1 | |
**Total: 9 marks**
---2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{2b891a9c-3abe-4e88-ba94-b6abcb37b4c3-04_682_853_283_543}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
Figure 2 represents part of the smooth rectangular floor of a sports hall. A ball is at $B$, 4 m from one wall of the hall and 5 m from an adjacent wall. These two walls are smooth and meet at the corner $C$. The ball is kicked so that it travels along the floor, bounces off the first wall at the point $X$ and hits the second wall at the point $Y$. The point $Y$ is 7.5 m from the corner $C$.\\
The coefficient of restitution between the ball and the first wall is $\frac { 3 } { 4 }$.\\
Modelling the ball as a particle, find the distance $C X$.
\hfill \mbox{\textit{Edexcel M4 2011 Q2 [9]}}