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## Homework Statement

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

C

_{d}= .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.

## Homework Equations

Eq. 1.8,

dv/dt = g-((C

_{d})/m)*v

^{2}

## The Attempt at a Solution

Used equation v(t

_{i}+1) = v(t

_{i}) + [g - (C

_{d}/m)*v(t

_{i})

^{2}](t

_{i}+1 - t

_{i})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 C

_{d}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(t

_{i}) as you can see from the first solution I have where t = 0, which may or may not be horribly wrong.

Thanks, much appreciated.