The royal gorge bridge over the arkansas river is 393 m above the river. a bungee jumper of mass 150 kg has an elastic cord of length 78 m attached to her feet. assume the cord acts like a spring of force constant k. the jumper leaps, barely touches the water, and after numerous ups and downs comes to rest at a height h above the water. the acceleration of gravity is 9.81 m/s². find h. answer in units of m.

188.7 m

Explanation:

height of bridge above water (h) = 393 m

mass of bungee jumper (m) = 150 kg

length of cord (L) = 78 m

acceleration due to gravity (g) = 9.8 m/s  

initial energy = mgh = 150 x 9.8 x 393 = 577,710 J

since the jumper barely touches the water, the maximum extension of the cord (x) = 393 - 78 = 315 m

from the conservation of energy mgh =

therefore

577,710 =

k = 11.64 N/m

from Hooke's law, force (f) = kx' ⇒ mg = kx'

where x' is the extension of the cord when it comes to rest

150 x 9.8 = 11.64 × x'

x' = 126.3 m

the final height at which the cord comes to a rest = height of the bridge - length of the cord - extension of the cord when it comes to rest

the final height at which the cord comes to a rest = 393  - 78 - 126.3 = 188.7 m

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