5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0da9cd5b-6f6f-4607-bd4f-c8ae164466ae-16_758_1399_280_333}
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\caption{Figure 1}
\end{figure}
A smooth uniform sphere \(S\) of mass \(m\) is moving with speed \(U\) on a smooth horizontal plane. The sphere \(S\) collides obliquely with another uniform sphere of mass \(M\) which is at rest on the plane. The two spheres have the same radius.
Immediately before the collision the direction of motion of \(S\) makes an angle \(\alpha\), where \(0 < \alpha < 90 ^ { \circ }\), with the line joining the centres of the spheres.
Immediately after the collision the direction of motion of \(S\) makes an angle \(\beta\) with the line joining the centres of the spheres, as shown in Figure 1.
The coefficient of restitution between the spheres is \(e\).
- Show that \(\tan \beta = \frac { ( m + M ) \tan \alpha } { ( m - e M ) }\)
Given that \(m = e M\),
- show that the directions of motion of the two spheres immediately after the collision are perpendicular.