3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a4cdf2b0-8dd0-4c12-9259-95b78875c6cb-05_643_1155_118_360}
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\caption{Figure 2}
\end{figure}
Two smooth uniform spheres \(A\) and \(B\), of equal radius \(r\), have masses \(3 m\) and \(2 m\) respectively. The spheres are moving on a smooth horizontal plane when they collide. Immediately before the collision they are moving with speeds \(u\) and \(2 u\) respectively. The centres of the spheres are moving towards each other along parallel paths at a distance \(1.6 r\) apart, as shown in Figure 2.
The coefficient of restitution between the two spheres is \(\frac { 1 } { 6 }\).
Find, in terms of \(m\) and \(u\), the magnitude of the impulse received by \(B\) in the collision.