Edexcel M4 2016 June — Question 2 9 marks

Exam BoardEdexcel
ModuleM4 (Mechanics 4)
Year2016
SessionJune
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicOblique and successive collisions
TypeBall between two walls, successive rebounds
DifficultyChallenging +1.2 This is a standard M4 mechanics problem requiring systematic application of coefficient of restitution formulas to two successive wall collisions. While it involves multiple steps and careful angle tracking, the method is routine: resolve velocities parallel and perpendicular to each wall, apply e for perpendicular components, and use the geometric constraint that the final direction is parallel to the initial direction. The algebra is straightforward once set up correctly.
Spec6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact

2. Figure 2 A small spherical ball \(P\) is at rest at the point \(A\) on a smooth horizontal floor. The ball is struck and travels along the floor until it hits a fixed smooth vertical wall at the point \(X\). The angle between \(A X\) and this wall is \(\alpha\), where \(\alpha\) is acute. A second fixed smooth vertical wall is perpendicular to the first wall and meets it in a vertical line through the point \(C\) on the floor. The ball rebounds from the first wall and hits the second wall at the point \(Y\). After \(P\) rebounds from the second wall, \(P\) is travelling in a direction parallel to \(X A\), as shown in Figure 2. The coefficient of restitution between the ball and the first wall is \(e\). The coefficient of restitution between the ball and the second wall is ke. Find the value of \(k\).
2. \includegraphics[max width=\textwidth, alt={}, center]{b01b3a41-3ed1-4104-b20d-4cfb845df4a1-03_582_645_118_648}

I apologize, but the content provided appears to be blank pages and formatting elements from a mark scheme document rather than actual marking criteria. The text consists of:
- Page headers and footers
- "DO NOT WRITE IN THIS AREA" warnings (repeated in reverse)
- "Turn over" instruction
- Multiple blank lines for answer space
- A reference to "Question 6 continued"
There is no actual mark scheme content (no marking points like M1, A1, B1, etc., and no question criteria) to clean up or convert.
Could you please provide the actual mark scheme content that needs to be cleaned? It should contain the marking annotations and criteria for the question.
I apologize, but the content provided appears to be blank pages and formatting elements from a mark scheme document rather than actual marking criteria. The text consists of:

- Page headers and footers
- "DO NOT WRITE IN THIS AREA" warnings (repeated in reverse)
- "Turn over" instruction
- Multiple blank lines for answer space
- A reference to "Question 6 continued"

There is no actual mark scheme content (no marking points like M1, A1, B1, etc., and no question criteria) to clean up or convert.

Could you please provide the actual mark scheme content that needs to be cleaned? It should contain the marking annotations and criteria for the question.
2.

Figure 2

A small spherical ball $P$ is at rest at the point $A$ on a smooth horizontal floor. The ball is struck and travels along the floor until it hits a fixed smooth vertical wall at the point $X$. The angle between $A X$ and this wall is $\alpha$, where $\alpha$ is acute. A second fixed smooth vertical wall is perpendicular to the first wall and meets it in a vertical line through the point $C$ on the floor. The ball rebounds from the first wall and hits the second wall at the point $Y$. After $P$ rebounds from the second wall, $P$ is travelling in a direction parallel to $X A$, as shown in Figure 2. The coefficient of restitution between the ball and the first wall is $e$. The coefficient of restitution between the ball and the second wall is ke.

Find the value of $k$.\\
2.\\
\includegraphics[max width=\textwidth, alt={}, center]{b01b3a41-3ed1-4104-b20d-4cfb845df4a1-03_582_645_118_648}

\hfill \mbox{\textit{Edexcel M4 2016 Q2 [9]}}