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Selene Routley
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You need to research the mechanics of drag and the Drag Co-efficient (start with this wiki page).

A simple model (where drag is a Ram Pressure) holds the drag to be proportional to the square of the speed. This can be justified on simple momentum conservation grounds, in the case of pure ram pressure. The drag co-efficient is an empirically-found "fudge factor" that multiplies the pure ram pressure to get the drag.

So, if the body is falling straight down, the nett force on it downwards is

$$F_\downarrow = m\,g - \frac{1}{2}\,\rho\,A\,c_d\,v^2\tag{1}$$

where $\rho$ is the fluid (air) density, $A$ the body's horizontal cross-sectional area (the face area presented to the flow), $v$ the body's downwards speed and $c_d$ the drag co-efficient. You can look these co-efficients up.

So if we put (1) into Newton's second law, you get a differential equation for the downward speed:

$$\frac{\mathrm{d}\,v}{\mathrm{d}t} = v\,\frac{\mathrm{d\,v}}{\mathrm{d}x} = g - \frac{\rho\,A\,c_d}{2\,m} v^2\tag{2}$$

where $x$ is the distance fallen. Something like Mathematica will give you explicit solutions to this equation. If you've studied differential equations, (2) is straightforward to solve by hand to get an analytic solution, too. Alternatively, you could integrate these equations numerically in your program, but I suspect the explicit solutions will be easier to get going.

The same ideas should give you enough to derive a vector description of dynamics if there is an initial horizontal component of velocity.

Selene Routley
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