The Royal Gorge bridge over the Arkansas River is 360 m above the river. A bunge

Question

The Royal Gorge bridge over the Arkansas River is 360 m above the river.
A bungee jumper of mass 93 kg has an elastic cord of length 85 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.

A) Find h. Answer in units of m

B)Find the maximum speed of the jumper. Answer in units of m/s The Royal Gorge bridge over the Arkansas River is 360 m above the river.
A bungee jumper of mass 93 kg has an elastic cord of length 85 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.

A) Find h. Answer in units of m

B)Find the maximum speed of the jumper. Answer in units of m/s

Explanation / Answer

First, we need k
.5*k*(360-85)^2=93*9.81*360

k=2*93*9.81*360 /(360-85)^2
k=8.6859 N/m

when
k*x=93*9.81    x = 105
h=360-(85+x)
h=170 m
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b) max speed is achieved when
when the jumper is at height h

x=105m, therefore
.5*m*v^2-.5*k*105^2=m*g*(360-h)
solve for v

v=sqrt(k*105^2/93+2*g*(360-h))
68.97 m/s
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