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.

1. 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 \(\frac { 1 } { 4 }\)
2. find \(x\) in terms of \(d\).
   

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