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

Particle \(P\) has mass \(m\text{ kg}\) and speed \(u\text{ m s}^{-1}\), momentum \(4\text{ N s}\) and kinetic energy 16 J.

(a) Find \(m,u\). [3]

\(P\) is now projected on a smooth horizontal surface at \(v\text{ m s}^{-1}\) towards stationary \(Q\), of mass 1.25 kg. After collision their velocities are \(w\) and \(2w\text{ m s}^{-1}\) respectively. The kinetic energy lost is 25 J.

(b) Find \(v,w\). [4]