Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2006-08-08 20:34:25

Matthijs
Guest

### Artillery shell

Hello all,

I'm looking for a function to calculate the altitude of an artillery shell after t seconds.

Variables are:
- 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 CrAV²
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.

help.. ?

## #2 2006-08-09 02:50:22

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Artillery shell

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..."

Offline

## #3 2006-08-20 02:12:19

Matthijs
Guest

### Re: Artillery shell

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.

## #4 2006-08-20 02:27:54

Matthijs
Member
Registered: 2006-08-20
Posts: 1

### Re: Artillery shell

(I registered - I'm only posting this line to subscribe to the thread)

When the only tool you have is a hammer, every problem will tend to look like a nail.

Offline