4. A small stone is projected vertically upwards from the point \(O\) and moves freely under gravity. The point \(A\) is 3.6 m vertically above \(O\). When the stone first reaches \(A\), the stone is moving upwards with speed \(11.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The stone is modelled as a particle.
- Find the maximum height above \(O\) reached by the stone.
- Find the total time between the instant when the stone was projected from \(O\) and the instant when it returns to \(O\).
- Sketch a velocity-time graph to represent the motion of the stone from the instant when it passes through \(A\) moving upwards to the instant when it returns to \(O\). Show, on the axes, the coordinates of the points where your graph meets the axes.