Question

Consider a free-falling bungee jumper whose vertical velocity is given by (1) dv/dt = g - (cd/m)v2 The drag coefficient cd is actually not constant but increases as the bungee jumper falls because air is more dense lower in the atmosphere. We suppose that (2) dcd /dz = cd/H where H is a scale height of the atmosphere. (Note that v = dz/dt.) Suppose that g = 10 m s-2, m = 60 kg, and H = 8 × 103 m. The initial conditions at t = 0 s are v = 0 m s-1 and cd = 0.2 kg m-1. We want to estimate v at some later time(s). (a) Show how you would apply Euler's method to solve this problem

Answer 1

this is what i think is the answer is this correct ??? So i know that the analytical solution would be v(t) = sqrt(gm/cd) tanh(sqrt(gcd/m)t) And the Euler method would be Vi+1=Vi + Fi (Tn+1 - Tn) then for dv/dt = g - (cd/m)v2 we would have something like Vi+1=Vi + h(g - (cd/m)v^2) where initial condition Vi(0)=0(given) but for dcd /dz = cd/H since v=dz/dt can we assume that dcd/dt=(cd/H)v where CDi+1=CDi +h(CD*v/H) where initial condition Cd(0)=0.2(given)