Analytical solution to bungee jumper problem.
Given time series as a vector, parameters mass and drag coefficient, and gravity coefficient, compute values of bungee jumper velocity (downward speed) at given times. Assume input values are in consistent units.
Problem Statement (Chapra, page 7): A bungee jumper with a mass of 68.1 kg leaps from a stationary hot air balloon. Use Eq. (1.9) to compute velocity for the first 12 s of free fall. Also determine the terminal velocity that will be attained for an infinitely long cord (or alternatively, the jumpmaster is having a particularly bad day!). Use a drag coefficient of 0.25 kg/m.
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The formula #1.9 is given by https://www.sccollege.edu/Departments/MATH/Documents/Math%20180/03-11-054_Hyperbolic_Functions.pdf (If this link becomes unavailable, Google free-fall velocity hyperbolic tangent)