7 A particle \(P\) is projected with speed \(\mathrm { Vms } ^ { - 1 }\) at an angle \(75 ^ { \circ }\) above the horizontal from a point \(O\) on a horizontal plane. It then moves freely under gravity.
- Show that the total time of flight, in seconds, is \(\frac { 2 \mathrm {~V} } { \mathrm {~g} } \sin 75 ^ { \circ }\).
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 \(\frac { 3 } { 5 }\). - Explain why the total time of flight is unchanged.
- Find an expression for \(V\) in terms of \(g\).
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