A 66.0 kg bungee jumper is standing on a tall platform ( h 0 = 53 m), as indicat

Question

A 66.0 kg bungee jumper is standing on a tall platform (h0 = 53 m), as indicated in Figure 10.36. The bungee cord has an unstrained length of L0 = 12 m, and when stretched, behaves like an ideal spring with a spring constant of k = 62.5 N/m. The jumper falls from rest, and the only forces acting on him are his weight and, for the latter part of the descent, the elastic force of the bungee cord.

A 66.0 kg bungee jumper is standing on a tall platform (h0 = 53 m), as indicated in Figure 10.36. The bungee cord has an unstrained length of L0 = 12 m, and when stretched, behaves like an ideal spring with a spring constant of k = 62.5 N/m. The jumper falls from rest, and the only forces acting on him are his weight and, for the latter part of the descent, the elastic force of the bungee cord. What is his maximum speed during the fall? How high above the water is he when he reaches this speed? How high above the water is he when he reaches the lowest point in the fall?

Explanation / Answer

1. max. speed , mgL0 = 1/2 mv^2

v = [2*9.8*12]^1/2 = 15.33m/s

2. at max speed, he is at 53-12 = 41m, as after that mg is opposed by elastic force.

3. At lowest point, kx = mg

  

x = 10.56m

so total 12+10.56 = 22.56m

at lowest point he is at 53 - 22.56 = 30.44m from water

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