1. A small stone is projected vertically upwards with speed \(39.2 \mathrm {~ms} ^ { - 1 }\) from a point \(O\).

The stone is modelled as a particle moving freely under gravity from when it is projected until it hits the ground 10s later. Using the model, find

1. the height of \(O\) above the ground,
2. the total length of time for which the speed of the stone is less than or equal to \(24.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
3. State one refinement that could be made to the model that would make your answer to part (a) more accurate.