6. A smooth sphere \(A\) of mass \(m\) is moving with speed \(u\) on a smooth horizontal table when it collides directly with another smooth sphere \(B\) of mass \(3 m\), which is at rest on the table. The coefficient of restitution between \(A\) and \(B\) is \(e\). The spheres have the same radius and are modelled as particles.

1. Show that the speed of \(B\) immediately after the collision is \(\frac { 1 } { 4 } ( 1 + e ) u\).
2. Find the speed of \(A\) immediately after the collision. Immediately after the collision the total kinetic energy of the spheres is \(\frac { 1 } { 6 } m u ^ { 2 }\).
3. Find the value of \(e\).
4. Hence show that \(A\) is at rest after the collision.