6. A particle \(P\) is projected from a fixed point \(A\) with speed \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\alpha\) above the horizontal and moves freely under gravity. As \(P\) passes through the point \(B\) on its path, \(P\) is moving with speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\beta\) below the horizontal.

1. By considering energy, find the vertical distance between \(A\) and \(B\). Particle \(P\) takes 1.5 seconds to travel from \(A\) to \(B\).
2. Find the size of angle \(\alpha\).
3. Find the size of angle \(\beta\).
4. Find the length of time for which the speed of \(P\) is less than \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).