Energy considerations in solving a bungee jumper question

[Toranc3]

Homework Statement

A bungee cord is 30.0 m long and, when stretched a distance x, it exerts a restoring force of magnitude kx. Your father-in-law (mass 95 kg) stands on a platform 45.0 m above the ground, and one end of the cord is tied securely to his ankle and the other end to the platform. You have promised him that when he steps off the platform he will fall a maximum distance of only 41.0 m before the cord stops him. You had several bungee cords to select from, and you tested them by stretching them out, tying one end to a tree, and pulling on the other end with a force of 380 N.

When you do this, what distance will the bungee cord that you should select have stretched?

Homework Equations

F=kx

K+U=K+U

The Attempt at a Solution

In this sentence "You have promised him that when he steps off the platform he will fall a maximum distance of only 41.0 m before the cord stops him." Does it mean that his velocity is zero there? I am confused with this sentence.

Here is what I have but this is wrong.

K1+U1=K2+U2
my point 1 is when he is at the top, y=45m and point 2 is where he is at the bottom, y=41m.

mgy1=mgy2 +1/2k(x)^2
(95)(9.8)(45)=(95)(9.8)(41) + 1/2k(11)^2

What am I doing wrong?

 

[haruspex]

In this sentence "You have promised him that when he steps off the platform he will fall a maximum distance of only 41.0 m before the cord stops him." Does it mean that his velocity is zero there?

Yes

.
where he is at the bottom, y=41m.

When he has fallen 41m, what will be his height from the ground?

 

[Toranc3]

Yes
When he has fallen 41m, what will be his height from the ground?

Would it be 4m?

 

[haruspex]

Yes, so y=4m at that point.

 

[Nickie]

I would approach this problem by first considering the energy involved in the bungee jumper's motion. The potential energy at the top of the platform is converted to kinetic energy as he falls, and then back to potential energy as the bungee cord stretches and pulls him back up. This energy conversion can be described by the equation K1+U1=K2+U2, where K is kinetic energy and U is potential energy.

To find the correct bungee cord to use, we need to consider the maximum distance the jumper will fall (41m) and the force exerted on the cord (380N). Using the equation F=kx, we can solve for the spring constant k.

F=kx
380N=k(41m)
k=9.27 N/m

Now, we can use this value of k to calculate the distance the bungee cord will stretch when it exerts a force of 380N.

F=kx
380N=(9.27 N/m)(x)
x=41.03m

Therefore, the bungee cord that should be selected will stretch 41.03m when a force of 380N is applied to it. This will ensure that the jumper falls a maximum distance of 41m, as promised.

In conclusion, energy considerations are crucial in solving this bungee jumper question. By understanding the conversion of potential and kinetic energy, and using the equation F=kx, we can determine the appropriate bungee cord to use for a safe and controlled jump.