8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{86a37170-046f-46e5-9c8c-06d5f98ca4fe-28_567_1406_244_333}
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\caption{Figure 5}
\end{figure}
Figure 5 represents the plan view of part of a smooth horizontal floor, where \(R S\) and \(S T\) are smooth fixed vertical walls. The vector \(\overrightarrow { R S }\) is in the direction of \(\mathbf { i }\) and the vector \(\overrightarrow { S T }\) is in the direction of \(( 2 \mathbf { i } + \mathbf { j } )\).
A small ball \(B\) is projected across the floor towards \(R S\). Immediately before the impact with \(R S\), the velocity of \(B\) is \(( 6 \mathbf { i } - 8 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). The ball bounces off \(R S\) and then hits \(S T\).
The ball is modelled as a particle.
Given that the coefficient of restitution between \(B\) and \(R S\) is \(e\),
- find the full range of possible values of \(e\).
It is now given that \(e = \frac { 1 } { 4 }\) and that the coefficient of restitution between \(B\) and \(S T\) is \(\frac { 1 } { 2 }\)
- Find, in terms of \(\mathbf { i }\) and \(\mathbf { j }\), the velocity of \(B\) immediately after its impact with \(S T\).