⚠️Our tutors found the solution shown to be helpful for the problem you're searching for. We don't have the exact solution yet.

Starting from rest, a 64.0-kg person bungee jumps from a tethered hot-air balloon 65.0 m above the ground. The bungee cord has negligible mass and unstretched length 25.8 m. One end is tied to the basket of the balloon and the other end to a harness around the person’s body. The cord is modeled as a spring that obeys Hooke’s law with a spring constant of 81.0 N/m, and the person’s body is modeled as a particle. The hot-air balloon does not move.

(a) Express the gravitational potential energy of the person–Earth system as a function of the person’s variable height y above the ground.

(b) Express the elastic potential energy of the cord as a function of y.

(c) Express the total potential energy of the person–cord–Earth system as a function of y.

(d) Plot a graph of the gravitational, elastic, and total potential energies as functions of y.

(e) Assume air resistance is negligible. Determine the minimum height of the person above the ground during his plunge.

(f) Does the potential energy graph show any equilibrium position or positions? If so, at what elevations? Are they stable or unstable?

(g) Determine the jumper’s maximum speed.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Force & Potential Energy concept. You can view video lessons to learn Force & Potential Energy. Or if you need more Force & Potential Energy practice, you can also practice Force & Potential Energy practice problems.

What textbook is this problem found in?

Our data indicates that this problem or a close variation was asked in Physics for Scientists and Engineers - Serway Calc 9th Edition. You can also practice Physics for Scientists and Engineers - Serway Calc 9th Edition practice problems.