7 A particle is projected from a point \(O\) on a smooth plane which is inclined at \(30 ^ { \circ }\) to the horizontal. The particle is projected down the plane with velocity \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(40 ^ { \circ }\) above the plane and first strikes it at a point \(A\). The motion of the particle is in a vertical plane containing a line of greatest slope of the inclined plane.
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1. Show that the time taken by the particle to travel from \(O\) to \(A\) is $$\frac { 20 \sin 40 ^ { \circ } } { g \cos 30 ^ { \circ } }$$
2. Find the components of the velocity of the particle parallel to and perpendicular to the slope as it hits the slope at \(A\).
3. The coefficient of restitution between the slope and the particle is 0.5 . Find the speed of the particle as it rebounds from the slope.