Upward vertical movement with air drag.

\hat{} Hi, here's the problem: "upward vertical movement with air drag"

speed = v; initial speed at t0 = v0; initial height x0 = 0

x= vertical distance travelled

force gravity Fg=-m.g

force drag Fd=-k.v^2 (k=ct describing air, shape of object,...)

F=m.a :

--> m.a=-m.g-k.v^2 (a=x'' and y=x' and devide by mass m)

--> x'' = -g - (k/m).x'^2

--> x'' + (k/m).x'^2 = -g

--> what is the function of x in time, and of v in time?

That's a DE with second order and second degree, never learned this but am eager to learn it, searched som sites about DE but didn't easily find a way to solve this...

thanks for the help!

Bart