I'm looking for a function to calculate the altitude of an artillery shell after t seconds.
- Initial vertical velocity; V0
- Gravity; g = 9,81 m/s² (it's actually a constant in my case)
- Air friction, which is a function of velocity and a series of constants; f = - 0.5 CrAV²
In which r is the air density, C is the drag coefficient, A is the surface of the object, and V is the current velocity.
Without air friction, I would be able to find the solution myself.
But I'm totally lost trying to find a solution that incorporates air friction.
Not too hard of a problem. I just need to know, are you studying differential equations?
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
Well... I have been. About 12 years ago.
I know I used integrals to calculate acceleration, time dilatation etc. during interstellar-travel. As simple and fun I found it back then, my current knowledge on the subject of limits, differentials and integrals approaches zero.
Recently, I dusted off my old math book, but I lost my notes (too bad, as I had an excellent teacher).
I managed to get hold of a new math book that describes limits, differentials and integrals. Now I'm slowly eating my way back into the matter.