Question

Kate, a bungee jumper, wants to jump off the edge of a bridge that spans a river below.

Kate has a mass m, and the surface of the bridge is a height h above the water. The bungee cord,
which has length L when unstretched, will first straighten and then stretch as Kate falls.

Assume the following:
•The bungee cord behaves as an ideal spring once it begins to stretch, with spring constant k.
•Kate doesn't actually jump but simply steps off the edge of the bridge and falls straight downward.
•Kate's height is negligible compared to the length of the bungee cord. Hence, she

Part A
How far below the bridge will Kate eventually be hanging, once she stops oscillating and comes finally to rest?
Assume that she doesn't touch the water.

Answer 1

Answer: Kate doesn't actually jump but simply steps off the edge of the bridge and falls straight downward

Step-by-step explanation:

Answer 2

To find how far below the bridge Kate will eventually be hanging, you can use the principle of conservation of energy. At the instant that Kate steps off the bridge, she has gravitational potential energy mgh, where m is her mass, g is the acceleration due to gravity, and h is the height of the bridge. When she comes to rest, all of her gravitational potential energy has been converted to elastic potential energy stored in the bungee cord, which can be expressed as (1/2)kx^2, where k is the spring constant of the bungee cord and x is the amount that the cord has stretched beyond its unstretched length L.

Setting these two expressions equal to each other and solving for x, you get:

mgh = (1/2)kx^2
x = sqrt(2mgh/k)

Once Kate has stretched the bungee cord by this amount, the force of the cord pulling upward on her will balance the force of gravity pulling downward on her, and she will come to rest. At this point, she will be hanging a distance y below the bridge, where y = L + x.

So, the final answer is:

y = L + sqrt(2mgh/k)