A ball is projected vertically upwards with a speed of \(14.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point which is 49 m above horizontal ground. Modelling the ball as a particle moving freely under gravity, find
the greatest height, above the ground, reached by the ball,
the speed with which the ball first strikes the ground,
the total time from when the ball is projected to when it first strikes the ground.