8. A particle \(A\) of mass \(3 m\) lies at rest on a smooth horizontal floor. A particle \(B\) of mass \(2 m\) is moving in a straight line on the floor with speed \(u\) when it collides directly with \(A\). The coefficient of restitution between \(A\) and \(B\) is \(e\). As a result of the collision the direction of motion of \(B\) is reversed.

1. Find an expression, in terms of \(u\) and \(e\), for
   1. the speed of \(A\) immediately after the collision,
   2. the speed of \(B\) immediately after the collision. The particle \(A\) subsequently strikes a smooth vertical wall. The wall is perpendicular to the direction of motion of \(A\). The coefficient of restitution between \(A\) and the wall is \(\frac { 1 } { 7 }\) There is a second collision between \(A\) and \(B\).
2. Show that \(\frac { 2 } { 3 } < e < \frac { 16 } { 19 }\)