5. A vertical cliff is 73.5 m high. Two stones \(A\) and \(B\) are projected simultaneously. Stone \(A\) is projected horizontally from the top of the cliff with speed \(28 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Stone \(B\) is projected from the bottom of the cliff with speed \(35 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\alpha\) above the horizontal. The stones move freely under gravity in the same vertical plane and collide in mid-air. By considering the horizontal motion of each stone,

1. prove that \(\cos \alpha = \frac { 4 } { 5 }\).
2. Find the time which elapses between the instant when the stones are projected and the instant when they collide.