5. A cricket ball of mass 0.3 kg is approaching a batsman at \({ } ^ { - } 30 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The batsman hits the ball with a 1.5 kg bat moving with velocity \(15 \mathrm { i } \mathrm { m } \mathrm { s } ^ { - 1 }\). Contact between bat and ball lasts for 0.2 seconds. Immediately after this, bat and ball move with velocities \(5 \mathbf { i } \mathrm {~ms} ^ { - 1 }\) and \(v \mathbf { i } \mathrm {~ms} ^ { - 1 }\) respectively.

1. Suggest a suitable model for the cricket ball.
2. Calculate the value of \(v\).
3. Find the magnitude of the force with which the batsman hits the ball.