2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a871044a-17c5-440d-8d8f-886939603dd4-06_524_638_255_717}
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\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,
- show that the value of \(e = \frac { 1 } { 4 }\)
- find the speed of the ball immediately after it hits \(B C\).
- Suggest two ways in which the model could be refined to make it more realistic.