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

I want to numerically simulate a fall with air drag. In class, we used these equations to produce a table simulating free fall (using a ti calculator):

When I compared that system with the curve produced by the direct equation, x=1/2at², I noticed a slight error. After looking at the equations again, I figured that the error came from the fact that I used vCode (Text):dt=0.1s

a=9.81m/s²

t[SUB]n+1[/SUB]=t[SUB]n[/SUB]+dt

v[SUB]n+1[/SUB]=v[SUB]n[/SUB]+a*dt

x[SUB]n+1[/SUB]=x[SUB]n[/SUB]+v[SUB]n[/SUB]*dt_{n}, so the curve would always be a bit lower than 1/2at². So I fixed that by changing the Equation to

Now I want to create a similar system but with air drag. As before, my physics book says that I should use vCode (Text):x[SUB]n+1[/SUB]=x[SUB]n[/SUB]+((v[SUB]n+1[/SUB]+v[SUB]n[/SUB])/2)*dt_{n}and not (v_{n}+v_{n+1})/2. But the book was wrong when it came to free fall, so I don't know which value to use for v. IthinkI should use (v_{n}+v_{n+1})/2. But since I don't know the direct equation this time (if there is one), I can't compare to the correct solution..

2a. Relevant equations

v=x/t

a=v/t

F=ma

F_{d}=b|v|^{m}

v_{E}=(mg/b)^{1/m}

a=g(1-v^{m}/v_{E}^{m})

F_{d}is the air drag

b and m are constants depending on the drag (I think in the case of air, m is about 2)

v_{E}is the end velocity the falling body will achieve

3. The attempt at a solution

These are the spreadsheets with the 2 systems:

http://dracayr.awardspace.com/physik.ods" [Broken]

http://dracayr.awardspace.com/physik.xls" [Broken]

dracayr

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# Fall with air drag

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