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\includegraphics[max width=\textwidth, alt={}, center]{c175972b-e298-4c86-bbef-3b05c6aca76f-08_412_339_260_897} A child of mass 35 kg is swinging on a rope. The child is modelled as a particle \(P\) and the rope is modelled as a light inextensible string of length 4 m . Initially \(P\) is held at an angle of \(45 ^ { \circ }\) to the vertical (see diagram).

1. Given that there is no resistance force, find the speed of \(P\) when it has travelled half way along the circular arc from its initial position to its lowest point.
2. It is given instead that there is a resistance force. The work done against the resistance force as \(P\) travels from its initial position to its lowest point is \(X \mathrm {~J}\). The speed of \(P\) at its lowest point is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find \(X\).