4. Two small balls, $A$ and $B$, are moving in opposite directions along the same straight line on smooth horizontal ground. The mass of $A$ is $2 m$ and the mass of $B$ is $3 m$. The balls collide directly. Immediately before the collision, the speed of $A$ is $2 u$ and the speed of $B$ is $u$. The coefficient of restitution between $A$ and $B$ is $e$, where $e > 0$

By modelling the balls as particles,
\begin{enumerate}[label=(\alph*)]
\item show that the speed of $B$ immediately after the collision is $\frac { 1 } { 5 } u ( 1 + 6 e )$.\\
(6)

After the collision with ball $A$, ball $B$ hits a smooth fixed vertical wall which is perpendicular to the direction of motion of $B$.

The coefficient of restitution between $B$ and the wall is $\frac { 5 } { 7 }$\\
Ball $B$ rebounds from the wall and there is a second direct collision between $A$ and $B$.
\item Find the range of possible values of $e$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2022 Q4 [10]}}