1.

\begin{figure}[h]
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\caption{Figure 1}
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\end{figure}

Two smooth uniform spheres $A$ and $B$, of equal radius, are moving on a smooth horizontal plane. Sphere $A$ has mass 2 kg and sphere $B$ has mass 3 kg . The spheres collide and at the instant of collision the line joining their centres is parallel to $\mathbf { i }$. Before the collision $A$ has velocity ( $3 \mathbf { i } - \mathbf { j }$ ) $\mathrm { m } \mathrm { s } ^ { - 1 }$ and after the collision it has velocity $( - 2 \mathbf { i } - \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$. Before the collision the velocity of $B$ makes an angle $\alpha$ with the line of centres, as shown in Fig. 1, where $\tan \alpha = 2$. The coefficient of restitution between the spheres is $\frac { 1 } { 2 }$.

Find, in terms of $\mathbf { i }$ and $\mathbf { j }$, the velocity of $B$ before the collision.\\
(9)\\

\hfill \mbox{\textit{Edexcel M4 2002 Q1 [9]}}