# Bungee jumping dynamics assignment

• Jess3

## Homework Statement

A formula has been determined: d=l+h+ (l(SRT(m(m+150))+m)/75), where d is the depth jumped to, l is the length of the rope, h is the height of the jumper and m is the mass of the person. The question is:
At present, the model does not include air resistance. Show and discuss all changes that would have to be made to the model to include air resistance, which is proportional to the velocity of the jumper.

b. Discuss the difficulties involved with the mathematics of this model.

## The Attempt at a Solution

I'm supposed to determine a constant of air resistance (which I have called b) from the information that Air resistance (which I have called J): is proportional to: velocity but I'm so stuck I have no direction

## Answers and Replies

Hello Jess,

Oops, according to the guidelines in PF we need you to at least make an attempt before we can help you. Just saying "dunno" isn't good enough. Also, we now have no idea at what level you need guidance. At high school level the derivation of the model in the exercise is already quite a task, and here you are asked to bring in a refinement and discuss the complications !

How do you think this "d=l+h+ (l(SRT(m(m+150))+m)/75)" was determined ? Where are ##g## and the spring constant of the chord ?

berkeman
To get you started, the jumper is in free fall until the rope stretches which occurs at its max, unstretched length (L). So, I would say that the velocity would be the length of the rope divided by elapsed time (v=L/t) or using one of the equations of motion and assuming the initial velocity is zero, velocity = acceleration * time (v=at). Air resistance not only is proportional to velocity but it is also proportional to shape.