5. Two small smooth spheres, \(P\) and \(Q\), of equal radius, have masses \(2 m\) and \(3 m\) respectively. The sphere \(P\) is moving with speed \(5 u\) on a smooth horizontal table when it collides directly with \(Q\), which is at rest on the table. The coefficient of restitution between \(P\) and \(Q\) is \(e\).

1. Show that the speed of \(Q\) immediately after the collision is \(2 ( 1 + e ) u\). After the collision, \(Q\) hits a smooth vertical wall which is at the edge of the table and perpendicular to the direction of motion of \(Q\). The coefficient of restitution between \(Q\) and the wall is \(f , 0 < f \leqslant 1\).
2. Show that, when \(e = 0.4\), there is a second collision between \(P\) and \(Q\). Given that \(e = 0.8\) and there is a second collision between \(P\) and \(Q\),
3. find the range of possible values of \(f\).