1.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b01b3a41-3ed1-4104-b20d-4cfb845df4a1-02_476_835_121_552}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A smooth uniform sphere \(A\) of mass \(m\) is moving on a smooth horizontal plane when it collides with a second smooth uniform sphere \(B\), which is at rest on the plane. The sphere \(B\) has mass \(4 m\) and the same radius as \(A\). Immediately before the collision the direction of motion of \(A\) makes an angle \(\alpha\) with the line of centres of the spheres, as shown in Figure 1. The direction of motion of \(A\) is turned through an angle of \(90 ^ { \circ }\) by the collision and the coefficient of restitution between the spheres is \(\frac { 1 } { 2 }\)
Find the value of \(\tan \alpha\).
1.
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