Tarzan swings on a vine from a cliff to rescue Jane, who is standing on the ground surrounded by snakes. His plan is to push off the cliff, grab Jane at the lowest point of his
swing, and carry them both to the safety of a nearby tree (see figure). Tarzan's mass is 93.2
kg, Jane's mass is 59.2 kg, the height of the lowest limb of the target tree is 24.5 m, and
Tarzan is initially standing on a cliff of height 28.5 m. The length of the vine is 23 m. Tarzan
has designed a spring launcher (k = 5950 N/m) to launch himself into action.
1) How far must he compress the spring if he and Jane are to make it to the tree
limb successfully?
2) Giving up on his spring, Tarzan starts from rest and swings down. What
impulse must he impart to Jane to save just her? What effect does this have on
Tarzan? How can he do this?

the answer is b i think

chemical energy --> gravitational potential energy --> kinetic energy --> elastic potential energy --> gravitational potential energy

explanation:

when emma starts the hike, the chemical energy stored in her body is used to climb up the mountain, and so she gains gravitational potential energy (because at the end, she will be at a higher height h above the ground). then she goes bungee jumping: as she falls, this gravitational potential energy is converted into kinetic energy (because her speed increases as she falls down), until the point when the rope stretches, and she stops moving. at that moment, all the kinetic energy is converted into elastic potential energy due to the stretching of the rope. then, this energy is released because the rope returns to its natural length, and emma gains a small increase in altitude , so she gains some gravitational potential energy.