4 For a bungee jump, a girl is joined to a fixed point \(O\) of a bridge by an elastic rope of natural length 25 m and modulus of elasticity 1320 N . The girl starts from rest at \(O\) and falls vertically. The lowest point reached by the girl is 60 m vertically below \(O\). The girl is modelled as a particle, the rope is assumed to be light, and air resistance is neglected.
- Find the greatest tension in the rope during the girl's jump.
- Use energy considerations to find
(a) the mass of the girl,
(b) the speed of the girl when she has fallen half way to the lowest point.