\begin{enumerate} \item By burning a charge, a cannon fires a cannon ball of mass 12 kg horizontally. As the cannon ball leaves the cannon, its speed is \(600 \mathrm {~ms} ^ { - 1 }\). The recoiling part of the cannon has a mass of 1600 kg .

1. Determine the speed of the recoiling part immediately after the cannon ball leaves the cannon.
2. Find the energy created by the burning of the charge. State any assumption you have made in your solution and briefly explain how the assumption affects your answer.
3. Calculate the constant force needed to bring the recoiling part to rest in 1.2 m . State, with a reason, whether your answer is an overestimate or an underestimate of the actual force required. \item A particle \(P\), of mass 3 kg , is attached to a fixed point \(O\) by a light inextensible string of length 4 m . Initially, particle \(P\) is held at rest at a point which is \(2 \sqrt { 3 } \mathrm {~m}\) horizontally from \(O\). It is then released and allowed to fall under gravity.