Edexcel FM1 2019 June — Question 2

Exam BoardEdexcel
ModuleFM1 (Further Mechanics 1)
Year2019
SessionJune
TopicMomentum and Collisions 2

2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a871044a-17c5-440d-8d8f-886939603dd4-06_524_638_255_717} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 represents the plan view of part of a horizontal floor, where \(A B\) and \(B C\) are fixed vertical walls with \(A B\) perpendicular to \(B C\). A small ball is projected along the floor towards \(A B\) with speed \(6 \mathrm {~ms} ^ { - 1 }\) on a path that makes an angle \(\alpha\) with \(A B\), where \(\tan \alpha = \frac { 4 } { 3 }\). The ball hits \(A B\) and then hits \(B C\).
Immediately after hitting \(A B\), the ball is moving at an angle \(\beta\) to \(A B\), where \(\tan \beta = \frac { 1 } { 3 }\)
The coefficient of restitution between the ball and \(A B\) is \(e\).
The coefficient of restitution between the ball and \(B C\) is \(\frac { 1 } { 2 }\)
By modelling the ball as a particle and the floor and walls as being smooth,
  1. show that the value of \(e = \frac { 1 } { 4 }\)
  2. find the speed of the ball immediately after it hits \(B C\).
  3. Suggest two ways in which the model could be refined to make it more realistic.