2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05f6f654-05e5-41d5-a6e4-11cd91a6df83-06_458_278_248_986}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A particle of mass em is at rest on a smooth horizontal plane between two smooth fixed parallel vertical walls, as shown in the plan view in Figure 2. The particle is projected along the plane with speed \(u\) towards one of the walls and strikes the wall at right angles. The coefficient of restitution between the particle and each wall is \(e\) and air resistance is modelled as being negligible.
Using the model,
- find, in terms of \(m , u\) and \(e\), an expression for the total loss in the kinetic energy of the particle as a result of the first two impacts.
Given that \(e\) can vary such that \(0 < e < 1\) and using the model,
- find the value of \(e\) for which the total loss in the kinetic energy of the particle as a result of the first two impacts is a maximum,
- describe the subsequent motion of the particle.