A small ball is projected vertically upwards from a point \(O\) with speed \(14.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The point \(O\) is 2.5 m above the ground. The motion of the ball is modelled as that of a particle moving freely under gravity.
Find
the maximum height above the ground reached by the ball,
the time taken for the ball to first reach a height of 1 m above the ground,
the speed of the ball at the instant before it strikes the ground for the first time.