It’s your birthday, and to celebrate you’re going to make your first bungee jump. You stand on a bridge 100 m above a raging river and attach a 30-m-long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of 40 N/m. Assume that your mass is 80 kg. After a long hesitation, you dive off the bridge. How far are you above the water when the cord reaches its maximum elongation?

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creamydhaka creamydhaka · Answer 1 · 2019-11-07T06:14:11+01:00

Answer:

[tex]X'=50.4\,m[/tex]

Explanation:

Given that:

Height of jump, [tex]h=100\,m[/tex]

length of elastic cord, [tex]l=30\,m[/tex]

spring constant of the cord, [tex]k=40\,N.m^{-1}[/tex]

mass of the body that jumps, [tex]m=80\,kg[/tex]

Force on the bungee elastic cord:

[tex]F=m.g[/tex]

[tex]F=80\times 9.8[/tex]

Now this force F will be responsible for the elongation in the elastic cord, so:

[tex]F=k.x[/tex] ............................(1)

where :

k = spring constant

x = extension in the elastic cord

using eq. (1)

[tex]80\times 9.8=40\times x[/tex]

[tex]x=19.6\,m[/tex]

So the cord stretches 19.6 meters more beyond its original length of 30 meters.

Hence, the remaining distance from the river surface at the bottom is:

[tex]X'=100-(30+19.6)[/tex]

[tex]X'=50.4\,m[/tex]