2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7eedd755-0dfd-4506-b7fd-23b9def4ebc8-04_508_780_258_584}
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\caption{Figure 1}
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The point \(A\) lies on a smooth horizontal floor between two fixed smooth parallel vertical walls \(W X\) and \(Y Z\), as shown in the plan view in Figure 1.
The distance between \(W X\) and \(Y Z\) is \(3 d\).
The distance of \(A\) from \(Y Z\) is \(d\).
A particle is projected from \(A\) along the floor with speed \(u\) towards \(Y Z\) in a direction perpendicular to \(Y Z\).
The coefficient of restitution between the particle and each wall is \(\frac { 2 } { 3 }\)
The time taken for the particle to move from \(A\), bounce off each wall once and return to A for the first time is \(T _ { 1 }\)
- Find \(T _ { 1 }\) in terms of \(d\) and \(u\).
The ball returns to \(A\) for the first time after bouncing off each wall once. The further time taken for the particle to move from \(A\), bounce off each wall once and return to \(A\) for the second time is \(T _ { 2 }\)
- Find \(T _ { 2 }\) in terms of \(d\) and \(u\).