Bungee Jump: 65 kg, 11m Rope, 36m Fall

[getalifebaby]

The girl is going on a bungee jump. She weighs 65 kg. The rope is 11m. In total, she fell 36 m. The first 11 m is free fall, and another 25m is simple harmonic motion.

1) k of rope
2)max spped
3)what point when she has max speed
4)amplitude of rope
5)how long does it take

Homework Equations

vf^2= 2ax
delta L= mg/k
_/(k/m) A- square rt of k/m times A

The Attempt at a Solution

initial velocity = 0
acceleration= 9.8m/s^2
1) k of rope
i got k for 25.48

2)max spped
max speed for free fall= 14.7m/s
V_max for rope= 15.65m/s
So do I add them up or just 15.65??!

3)what point when she has max speed
36m?

4)amplitude of rope
25m?

Thanks!

 

[Jokerhelper]

why don't you show us how you solved each step, starting with the first one?

 

[getalifebaby]

1) i used deltaL= mg/k

25m=65*9.8/k
k= 25.48

2) V_f^2=2(9.8)(11m)
V_f=14.7m/s for free fall
then
V_max= square rt of k/m *A
so sqr (25.48/65) *25= 15.65 m/s

Thanks

 

[Jokerhelper]

ok, for part 1 you have it right, but try using a more accurate value for g = 9.81 m/s². It will actually change your final answer.

For part two, when do you expect the person to reach her final speed? And also, how did you derive "V_max= square rt of k/m *A"?

 

[getalifebaby]

V_max when the rope reach maxium stretch.
I didnt derive it, it was a formula.

 

[Jokerhelper]

V_max when the rope reach maxium stretch.
I didnt derive it, it was a formula.

oh i see what you meant now. but using kinetic and elastic energy relationships only holds when there is only an elastic force present for a given period of time. Is this the case?

And plus, try to picture the scenario visually: once the elastic of the bungee jump is full stretched, what would you expect to happen? What would you guess her speed to be?