Bungee Jumping in France Problem?

Question

A bungee jumper makes a jump into the Gorge du Verdon in southern France from a platform 182 m above the bottom of the gorge. The jumper weighs 770 N and comes within 68 m of the bottom of the gorge. The cord's unstretched length is 30.0 m.

Assuming that the bungee cord follows Hooke's law when it stretches, find its spring constant. [Hint: The cord does not begin to stretch until the jumper has fallen 30.0 m.]

At what speed is the jumper falling when he reaches a height of 95 m above the bottom of the gorge?

Answer 1

182 - 68 = 114 m total fall
114 - 30 = 84 m stretch
v^2 - v0^2 = 2as
v0 = 0
K.E. = (1/2)mv^2 = mas = (1/2)kx^2
k = (2mas/x^2)
k = (2)(770)(30)/(84)^2)
k ≈ 6.5476 N/m

182 - 95 = 87 m
87 - 30 = 57 m
KE(30) = 770*30 = 23,100 N-m
∆KE ≈ (1/2)(6.5476)(57^2) ≈ 10,636.5762 N-m
v ≈ √(2)(10,636.5762)(9.80665)/(770)
v ≈ 16.46004 m/s ≈ 16.46 m/s