(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Bungee Jumping

l=natural length of rope

x=extension of rope

y=total distance fallen

m=mass,a=acceleration,v=velocity,g=acceleration due to gravity

k=air resistance co-efficient

Given data: The rope is stretched to twice its natural length by a mass of 75kg hanging at rest from its free end

The bungee jumper jumps off a bridge, as he falls, he experiences quadratic drag (kv^2), when the rope begins to extend, he also experiences a deceleration due to the tension in the rope. Find the maximum extension of the rope (x) with regards to the mass of the jumper (m) and the natural length of the rope(l).

Previous questions were without air resistance, which i worked out fine.

2. Relevant equations

F=ma (a=F/m)

T=jx (Hookes Law, j not k to avoid confusion with drag)

a=(d/dx)0.5x^2

a=v(dv/dx)

3. The attempt at a solution

General thought pattern:

Find the acceleration in terms of all the variables, from the acceleration, find the velocity through whichever means possible. Equal the velocity to 0, as this is when the extension will be at a maximum. Manipulate it into the form x=something.

Therefore:

a=acceleration due to gravity-acceleration due to tension - drag

a=g-(75g/lm)x -kv^2 ((75g/lm)x was found as the deceleration due to tension in one of the previous questions)

So i now have a formula for a in terms of the extension and the velocity, the trouble comes when i attempt to substitute a for either (d/dx)0.5x^2 or v(dv/dx). As the formula contains both x and v, im always left with trying to do either (75g/lm)x dv or kv^2 dx. The solution my teacher came up with was to treat x or v respectively as a constant(which they're not), but i dont really think that is the appropriate way to go about it.

I've also tried to use v^2 = u^2 +2as, but i then realised that only works for constant acceleration. I can calculate the velocity of the jumper when x=0, so im fine with tension or air resistance by themselves, it is when trying to put them both together where i become stuck.

So im really just trying to find a way to get started on this question without running into a brick wall, the only thing i can currently think of at this point is equating x to v somehow, but i have no idea if that will work or not.

Yes, this is for an assignment, i'm not asking for anyone to do it for me, im just looking for a place to start on this little piece of hell. If more info is needed, the assignment is here: http://www.qsa.qld.edu.au/downloads/senior/snr_maths_c_***_sample_2.pdf [Broken] (9th page) or just ask. Many thanks

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# Bungee Jumping-Tension+Air resistance with regards to max extension

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