| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2015 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Ball between two walls, successive rebounds |
| Difficulty | Standard +0.8 This M4 mechanics question requires careful vector decomposition of velocities in two sequential oblique wall collisions with coefficient of restitution 1/2. Students must correctly apply restitution perpendicular to each wall while preserving tangential components, then work with non-standard angles (60° and 120°). The multi-step nature, geometric complexity, and need for precise trigonometric reasoning place it above average difficulty, though it follows standard collision mechanics principles taught in M4. |
| Spec | 6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
Figure 4 represents the plan view of part of a smooth horizontal floor, where AB and BC are smooth vertical walls. The angle between AB and BC is $120°$. A ball is projected along the floor towards AB with speed $u$ m s$^{-1}$ on a path at an angle of $60°$ to AB. The ball hits AB and then hits BC. The ball is modelled as a particle. The coefficient of restitution between the ball and each wall is $\frac{1}{2}$
(a) Show that the speed of the ball immediately after it has hit AB is $\frac{7u}{4}$.
(6 marks)
The speed of the ball immediately after it has hit BC is $w$ m s$^{-1}$
(b) Find $w$ in terms of $u$.
(7 marks)7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{44066c44-e366-4f87-b1b2-c5a894e407fa-24_494_936_260_536}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}
Figure 4 represents the plan view of part of a smooth horizontal floor, where $A B$ and $B C$ are smooth vertical walls. The angle between $A B$ and $B C$ is $120 ^ { \circ }$. A ball is projected along the floor towards $A B$ with speed $u \mathrm {~m} \mathrm {~s} ^ { - 1 }$ on a path at an angle of $60 ^ { \circ }$ to $A B$. The ball hits $A B$ and then hits $B C$. The ball is modelled as a particle. The coefficient of restitution between the ball and each wall is $\frac { 1 } { 2 }$
\begin{enumerate}[label=(\alph*)]
\item Show that the speed of the ball immediately after it has hit $A B$ is $\frac { \sqrt { 7 } } { 4 } u$.
The speed of the ball immediately after it has hit $B C$ is $w \mathrm {~m} \mathrm {~s} ^ { - 1 }$
\item Find $w$ in terms of $u$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2015 Q7 [13]}}