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# Re: [Phys-L] Falling - the tale of a simple 1st degree non-linear ODE

• From: Carl Mungan <mungan@usna.edu>
• Date: Sun, 13 Jan 2019 14:00:16 -0500

Noting that the drag force has the same v^2 dependence as the KE, one can
straightforwardly integrate in 1D:

https://www.usna.edu/Users/physics/mungan/_files/documents/Publications/EJP3.pdf

On Sat, Jan 12, 2019 at 10:21 PM brian whatcott <betwys1@sbcglobal.net>
wrote:

I am pleased to use some of my dotage in answering questions on Quora.
I found this one strangely interesting:
How long does it take a jumper to reach terminal velocity?

An expression for the speed at which air drag equals weight goes like this:
jumpers mass times acceleration equals the net force provided by weight,
namely jumper's mass times g less air drag, namely 1/2 rho Cd A v^2
I spent way too much time in basing an estimate on the CR charging curve.
Apart from the similar curve, the rise time features differ greatly.
Casting around for better methods to plot this curve ~
Plugging the equation into Alpha solver on line?
A few lines of code in basic?
Mathematica?
Matlab?

It may be my imagination but the free use of Alpha online seems to be
more constrained than it used to be.
I could extract a plot, but the plotting was hit or miss - depending on
the coefficients I chose.
Basic code could provide a list of v against t but a good plot was lacking.
Mathematica was uncooperative, perhaps because I rarely use it.
Matlab had the ODE solvers but the examples were unhelpful.

Finally I looked up an MIT tutorial on using MATLAB with an example ODE
recipe which worked with my package, and took it from there.

https://i.imgur.com/K7KKlUG.jpg Matlab ODE
https://imgur.com/Eio6xs3 Alpha online

Brian W

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Carl E. Mungan, Professor of Physics 410-293-6680 (O) -3729 (F)
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