Hello everybody, I'm new to this forum and I have some difficulties when I try to solve a problem of free falling body when it is affected by gravitation and air resistance, which is equal to k*v^2/2 (k*y'^2/2). I need to find the equation of motion y(t) and the final velocity when t approaches infinity. I'm not that good at physics and differential equations, so I need your help.

I have tried to solve this by myself, but it was an intuition-like solving and the results I got aren't quite clear (I guess they aren't right too, hehe). So look what I got here:

http://img.photobucket.com/albums/v4...a/P2190001.jpg http://img.photobucket.com/albums/v4...a/P2190002.jpg
I got that a velocity when t approaches infinity is sqrt(2mg/k) and y(t) is some function you see in those pictures. As I don't have initial conditions, I can't determine those coefficients (it is said that a body is just falling).

I hope I wrote those exercises clearly and I stated this problem clearly too. I'm looking forward to seeing some answers / thoughts about that from you.