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Help with diffy eqn terminal vel problem 
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#1
Jan1006, 07:20 PM

P: 26

Hi,
So m*dv/dt = mg  kv^2, where m is skydiver mass, g acceleration due to gravity, and k> 0 related to amount of air resistance. So I want to find the analytical solution for v(t), with the assumption that v(0) = 0. I went all the way to integrating it with a partial fraction, but then got an answer drastically different from what the book got. Thanks... 


#2
Jan1006, 10:05 PM

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PF Gold
P: 39,361

It's hard to answer because you didn't show us what you did or what answer you got!



#3
Jan1106, 11:04 AM

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#4
Jan1106, 11:07 AM

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PF Gold
P: 12,016

Help with diffy eqn terminal vel problem
Please remember that the inverse of the hyperbolic tangent is a logarithmic expression.



#5
Jan1106, 06:47 PM

P: 585

If you just want the terminal velocity then set the acceleration (LHS) equal to zero and solve for v. I did a question like this about 1 or 2 years ago. If I remember correctly, the working is a little tedious but not too difficult. Obtaining the partial fraction decomposition is the difficult part, the integration and transposition should be straight forward.



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