Take \(g=10\,\mathrm{m\,s^{-2}}\).

A particle \(P\), of mass \(0.4\,\mathrm{kg}\), is projected vertically upwards from horizontal ground at \(10\,\mathrm{m\,s^{-1}}\).

(a) Find the greatest height reached. [2]

On returning to the ground, \(P\) bounces vertically upwards. It loses \(7.2\,\mathrm J\) of energy at its first impact with the ground.

(b) Find the time between its first and second ground impacts. [4]