12.\\[0pt]
[In this question $\mathbf { i }$ and $\mathbf { j }$ are perpendicular unit vectors in a horizontal plane.]\\
A smooth uniform sphere $A$ has mass 0.2 kg and another smooth uniform sphere $B$, with the same radius as $A$, has mass 0.4 kg .

The spheres are moving on a smooth horizontal surface when they collide obliquely. Immediately before the collision, the velocity of $A$ is $( 3 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ and the velocity of $B$ is $( - 4 \mathbf { i } - \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$

At the instant of collision, the line joining the centres of the spheres is parallel to $\mathbf { i }$ The coefficient of restitution between the spheres is $\frac { 3 } { 7 }$
\begin{enumerate}[label=(\alph*)]
\item Find the velocity of $A$ immediately after the collision.
\item Find the magnitude of the impulse received by $A$ in the collision.
\item Find, to the nearest degree, the size of the angle through which the direction of motion of $A$ is deflected as a result of the collision.
\end{enumerate}

\hfill \mbox{\textit{SPS SPS FM 2020 Q12 [12]}}