A particle \(P\) is projected with speed \(V\,\mathrm{m\,s}^{-1}\) at an angle \(75^{\circ}\) above the horizontal from a point \(O\) on a horizontal plane. It then moves freely under gravity.
(a) Show that the total time of flight, in seconds, is \(\frac{2 V}{g} \sin 75^{\circ}\).

A smooth vertical barrier is now inserted with its lower end on the plane at a distance 15 m from \(O\). The particle is projected as before but now strikes the barrier, rebounds and returns to \(O\). The coefficient of restitution between the barrier and the particle is \(\frac{3}{5}\).
(b) Explain why the total time of flight is unchanged.
(c) Find an expression for \(V\) in terms of \(g\).