4.
\begin{figure}[h]
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\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{4737e682-1e1d-4c1a-91c2-7d051cb43aac-3_417_986_303_534}
\end{figure}
Two smooth uniform spheres \(A\) and \(B\), of equal radius, are moving on a smooth horizontal plane. Sphere \(A\) has mass 3 kg and velocity \(( 2 \mathbf { i } + \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\), and sphere \(B\) has mass 5 kg and velocity \(( - \mathbf { i } + \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). When the spheres collide the line joining their centres is parallel to \(\mathbf { i }\), as shown in Fig. 2.
Given that the direction of \(A\) is deflected through a right angle by the collision, find
- the velocity of \(A\) after the collision,
- the coefficient of restitution between the spheres.