The Royal Gorge bridge over the Arkansas River is 310 m above the river. A 62-kg

Question

The Royal Gorge bridge over the Arkansas River is 310 m above the river. A 62-kg bungee jumper has an elastic cord with an unstressed length of 61 m attached to her feet. Assume that, like an ideal spring, the cord is massless and provides a linear restoring force when stretched. The jumper leaps, and at at her lowest point she barely touches the water. After numerous ascents and descents, she comes to rest at a height h above the water. Model the jumper as a point particle and assume that any effects of air resistance are negligible.

1)

(a) Find h.
km

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2)

(b) Find the maximum speed of the jumper.
m/s

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Explanation / Answer

k = (62 * 9.8 * 310) / (0.5 * (310 - 61)2)

k = 6.08

x = (62 * 9.8 / 6.08) = 99.93 m

h = L - d - x = 310 - 61 - 99.93

h = 149 m

-------------------------------------------------

E = 0 = 1/2 m v2 - mg (61 + x) + 1/2 kx2

v = sqrt(2 * 9.8 * 160.93 - 6.08 * 99.932/62)

v = 46.6 m/s

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