Register to reply

Help with diffy eqn terminal vel problem

by Ara macao
Tags: diffy, terminal
Share this thread:
Ara macao
#1
Jan10-06, 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...
Phys.Org News Partner Science news on Phys.org
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
HallsofIvy
#2
Jan10-06, 10:05 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,361
It's hard to answer because you didn't show us what you did or what answer you got!
saltydog
#3
Jan11-06, 11:04 AM
Sci Advisor
HW Helper
P: 1,593
Quote Quote by Ara macao
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...
Tell you what Ara, how about looking up Riccati equations. Now, can your equation be put in such form? If if can, then such a prespective may allow an easier approach to its solution.

arildno
#4
Jan11-06, 11:07 AM
Sci Advisor
HW Helper
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.
Benny
#5
Jan11-06, 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.


Register to reply

Related Discussions
Diffy Q word Problem ? Calculus & Beyond Homework 5
Mixing involving diffy q Calculus & Beyond Homework 1
Terminal velocity problem Introductory Physics Homework 3
#2 Variation of parameters with complemetry EQ (Diffy Q) Calculus & Beyond Homework 1
Iffy diffy q Introductory Physics Homework 10