Use \(g=10\text{ m s}^{-2}\).

Particles \(P,Q\), masses \(m\text{ kg},2\text{ kg}\), move freely on a smooth horizontal plane directly towards each other at speeds \(u\) and \(3u\). Their collision reverses both directions; immediately afterwards \(P\) has speed \(u/3\).

(a) Find the velocity of \(Q\) after collision in terms of \(m,u\), and show \(m>4.5\). [3]

\(Q\) subsequently hits a vertical wall perpendicular to its motion. Its speed after impact is a quarter of its speed before impact. There are no further collisions between \(P,Q\).

(b) Given \(m\) is an integer, find its largest possible value. [4]