For the second order drag model (Eq. 1.8), compute the velocity of a free-falling parachutist using Euler's method for the case where,
m = 80 kg
Cd = .25 kg/m
Perform the calculation from t = 0 to 20 with a step size of 1 s. Use an initial condition that the parachutist has an upward velocity of 20 m/s at t = 0. At t=10 s, assume that the chute is instantaneously deployed so that the drag coefficient jumps to 1.5 kg/m.
dv/dt = g-((Cd)/m)*v2
The Attempt at a Solution
Used equation v(ti+1) = v(ti) + [g - (Cd/m)*v(ti)2](ti+1 - ti)v
(Used in example in book, unfortunately no example w/ an initial condition with an "upward velocity" though)
Plugged in the values to achieve,
t = 0........... V = 20 + [9.81 - (.25/80)(0)2] *1 = 29.81m/s
t= 1............V = 29.81 + [9.81 - (.25/80)2]*1 = 36.51m/s
t =2.............V=36.51 + [9.81-(.25/80)2]*1 = 42.15 m/s
...so on until t = 10 where Cd changes from .25 to 1.5
Am I doing this right? I don't know how the "upward velocity = 20" works into this. I assumed that it is the initial v(ti) as you can see from the first solution I have where t = 0, which may or may not be horribly wrong.
Thanks, much appreciated.