Please answer this with a brief explanation. Thank you. You sign up for a bungee

Question

Please answer this with a brief explanation. Thank you.

You sign up for a bungee jump off a tall bridge. A thick rope with a fixed length of 20.0 m is tied to the bridge, and a bungee cord with an unstretched length of 11.0 m is then connected to the rope. The other end of the bungee cord is attached to your legs. You step off the bridge, falling from rest. The bungee cord does not start exerting any force on you until you have fallen a distance of 31 m (the sum of the rope's length and the unstretched length of the bungee cord). After that, it exerts an upward force on you that eventually brings you to rest, for an instant. Assume the bungee cord, when stretched, acts like an ideal spring, and take g 10 N/m to make he caculatos ease Your mass is 30.0 kg (a) You fall a total distance of 49.0 m before coming instantaneously to rest. Determine the spring constant of the bungee cord. N/m (b) How far below the bridge are you when you reach maximum speed? (c) Determine your maximum speed. mys

Explanation / Answer

(A) Applyng work - energy theorem,

work done by gravity + work done by elastic force = change in KE

m g d - k (d - 31)^2 / 2 = 0 - 0

30 x 10 x 49 = k (49 - 31)^2 /2

k = 90.7 N/m ....Ans

(b) maximum speed will be when,

Fnet = k x - m g = 0

90.7(x) = (30)(10)

x = 3.31 m

below the bridge = 31 + 3.31 = 34.4 m

(c) Applying work - energy theorem,

30 x 10x 34.4 - 90.7(3.31^2)2/2 = 30 (v^2 - 0)/2

v = 25.6 m/s

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