# Help with diffy eqn terminal vel problem

1. Jan 10, 2006

### 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...

2. Jan 10, 2006

### HallsofIvy

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

3. Jan 11, 2006

### saltydog

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.

4. Jan 11, 2006

### arildno

Please remember that the inverse of the hyperbolic tangent is a logarithmic expression.

5. Jan 11, 2006

### Benny

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.