5. Two smooth spheres $A$ and $B$, of equal radii, are moving on a smooth horizontal plane when they collide. Immediately after the collision sphere $A$ has velocity ( $- 2 \mathbf { i } - 5 \mathbf { j }$ ) $\mathrm { ms } ^ { - 1 }$ and sphere $B$ has velocity $( \mathbf { i } + 3 \mathbf { j } ) \mathrm { ms } ^ { - 1 }$. When the spheres collide, their line of centres is parallel to the vector $\mathbf { i }$ and the coefficient of restitution between the spheres is $\frac { 2 } { 5 }$. Sphere $A$ has mass 4 kg and sphere $B$ has mass 2 kg .
\begin{enumerate}[label=(\alph*)]
\item Find the velocity of $A$ and the velocity of $B$ immediately before the collision.

After the collision, sphere $A$ continues to move with velocity ( $- 2 \mathbf { i } - 5 \mathbf { j }$ ) $\mathrm { ms } ^ { - 1 }$ until it collides with a smooth vertical wall. The impulse exerted by the wall on $A$ is $32 \mathbf { j }$ Ns.
\item State whether the wall is parallel to the vector $\mathbf { i }$ or to the vector $\mathbf { j }$. Give a reason for your answer.
\item Find the speed of $A$ after the collision with the wall.
\item Calculate the loss of kinetic energy caused by the collision of sphere $A$ with the wall.
\end{enumerate}

\hfill \mbox{\textit{WJEC Further Unit 6 2022 Q5 [13]}}