| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2008 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Sphere rebounds off fixed wall obliquely |
| Difficulty | Standard +0.8 This M4 oblique collision problem requires resolving velocities parallel and perpendicular to the wall, applying the coefficient of restitution correctly to the normal component only, then using the geometric constraint that angles change from 2θ to θ. It demands careful vector resolution, understanding of restitution in 2D collisions, and algebraic manipulation involving trigonometric identities—significantly above average difficulty but standard for M4 level. |
| Spec | 6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Notes |
| \(u\cos2\theta = v\cos\theta\) | M1 A1 | |
| \(\frac{3}{8}u\sin2\theta = v\sin\theta\) | M1 A1 | |
| \(3\tan2\theta = 8\tan\theta\) | M1 | |
| \(\dfrac{6\tan\theta}{1-\tan^2\theta} = 8\tan\theta\) | M1 | |
| \(\tan^2\theta = \frac{1}{4} \quad (\tan\theta \neq 0)\) | ||
| \(\tan\theta = \frac{1}{2}\) | M1 A1 | Total: 8 |
## Question 4:
| Working/Answer | Marks | Notes |
|---|---|---|
| $u\cos2\theta = v\cos\theta$ | M1 A1 | |
| $\frac{3}{8}u\sin2\theta = v\sin\theta$ | M1 A1 | |
| $3\tan2\theta = 8\tan\theta$ | M1 | |
| $\dfrac{6\tan\theta}{1-\tan^2\theta} = 8\tan\theta$ | M1 | |
| $\tan^2\theta = \frac{1}{4} \quad (\tan\theta \neq 0)$ | | |
| $\tan\theta = \frac{1}{2}$ | M1 A1 | **Total: 8** |
---4.
\begin{figure}[h]
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\includegraphics[alt={},max width=\textwidth]{376d12ab-022c-4070-a1e0-88eacc2fe48e-2_451_357_1672_852}
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\caption{Figure 1}
\end{center}
\end{figure}
A small smooth ball $B$, moving on a horizontal plane, collides with a fixed vertical wall. Immediately before the collision the angle between the direction of motion of $B$ and the wall is $2 \theta$, where $0 ^ { \circ } < \theta < 45 ^ { \circ }$. Immediately after the collision the angle between the direction of motion of $B$ and the wall is $\theta$, as shown in Figure 1.
Given that the coefficient of restitution between $B$ and the wall is $\frac { 3 } { 8 }$, find the value of $\tan \theta$.\\
(8)\\
\hfill \mbox{\textit{Edexcel M4 2008 Q4 [8]}}