3 A particle \(P\) is projected vertically upwards with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point \(A\) which is 2.8 m above horizontal ground.

1. Find the greatest height above the ground reached by \(P\).
2. Find the length of time for which \(P\) is at a height of more than 3.6 m above the ground.
   The diagram shows a ring of mass 0.1 kg threaded on a fixed horizontal rod. The rod is rough and the coefficient of friction between the ring and the rod is 0.8 . A force of magnitude \(T \mathrm {~N}\) acts on the ring in a direction at \(30 ^ { \circ }\) to the rod, downwards in the vertical plane containing the rod. Initially the ring is at rest.
3. Find the greatest value of \(T\) for which the ring remains at rest.
4. Find the acceleration of the ring when \(T = 3\).