8. Two particles, $A$ and $B$, have masses $3 m$ and $4 m$ respectively. The particles are moving towards each other along the same straight line on a smooth horizontal surface. The particles collide directly. Immediately after the collision, $A$ and $B$ are moving in the same direction with speeds $\frac { u } { 3 }$ and $u$ respectively. In the collision, $A$ receives an impulse of magnitude 8mu.
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\item Find the coefficient of restitution between $A$ and $B$.

When $A$ and $B$ collide they are at a distance $d$ from a smooth vertical wall, which is perpendicular to their direction of motion. After the collision with $A$, particle $B$ collides directly with the wall and rebounds so that there is a second collision between $A$ and $B$. This second collision takes place at distance $x$ from the wall.

Given that the coefficient of restitution between $B$ and the wall is $\frac { 1 } { 4 }$
\item find $x$ in terms of $d$.\\

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\hfill \mbox{\textit{Edexcel M2 2021 Q8 [12]}}