4. The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) lie in a vertical plane, \(\mathbf { i }\) being horizontal and \(\mathbf { j }\) vertical. A ball of mass 0.1 kg is hit by a bat which gives it an impulse of \(( 3.5 \mathbf { i } + 3 \mathbf { j } )\) Ns. The velocity of the ball immediately after being hit is \(( 10 \mathbf { i } + 25 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).

1. Find the velocity of the ball immediately before it is hit. In the subsequent motion the ball is modelled as a particle moving freely under gravity. When it is hit the ball is 1 m above horizontal ground.
2. Find the greatest height of the ball above the ground in the subsequent motion. The ball is caught when it is again 1 m above the ground.
3. Find the distance from the point where the ball is hit to the point where it is caught.