4 A particle \(P\) is projected with speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) above the horizontal from a point \(O\) on horizontal ground. \(P\) subsequently bounces when it first strikes the ground at the point \(A\).

1. Find the time after projection when \(P\) first strikes the ground, and the distance \(O A\). When \(P\) bounces at \(A\) the horizontal component of the velocity of \(P\) is unchanged. The vertical component of velocity is \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) immediately after bouncing. \(P\) strikes the ground for the second time at \(B\) where it remains at rest.
2. Calculate the first and last times after projection at which the speed of \(P\) is \(18 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).