A particle \(P\) of mass \(3 m\) is moving in a straight line with speed \(2 u\) on a smooth horizontal table. It collides directly with another particle \(Q\) of mass \(2 m\) which is moving with speed \(u\) in the opposite direction to \(P\). The coefficient of restitution between \(P\) and \(Q\) is \(e\).
Show that the speed of \(Q\) immediately after the collision is \(\frac { 1 } { 5 } ( 9 e + 4 ) u\).
The speed of \(P\) immediately after the collision is \(\frac { 1 } { 2 } u\).
Show that \(e = \frac { 1 } { 4 }\).
The collision between \(P\) and \(Q\) takes place at the point \(A\). After the collision \(Q\) hits a smooth fixed vertical wall which is at right-angles to the direction of motion of \(Q\). The distance from \(A\) to the wall is \(d\).
Show that \(P\) is a distance \(\frac { 3 } { 5 } d\) from the wall at the instant when \(Q\) hits the wall.
Particle \(Q\) rebounds from the wall and moves so as to collide directly with particle \(P\) at the point \(B\). Given that the coefficient of restitution between \(Q\) and the wall is \(\frac { 1 } { 5 }\),
find, in terms of \(d\), the distance of the point \(B\) from the wall.