Among other things, Tim Nikias v2.0 wrote:

>> Ignoring friction and rotational energy, you'd simply be checking that
>> your potential energy matches your kinetic energy, wouldn't you? The
>> formulae for both are pretty straightforward.
> 
> Ehm, yeah, sure... Point is: I can't find those formulae. That aside, I
> just want the velocity approach, not energies etc, cause I don't know
> anything else of that particle beside it's velocity. Might be that I'm
> talking BS because I don't know which formulae you're talking about, but,
> for example, I've got a few formulae like "Height after object is thrown
> with that slope and that velocity with earth's gravity". What I want is
> something along the lines of "Velocity after object is rolled up/down a
> slope with that angle, velocity and gravity".

Kinetic energy: 1/2 * m * v^2
Potential energy: g * m * h

Total energy must be constant.

If the particle has velocity v1 at height h1, then at height h2 it should 
have:

1/2*m*(v1)^2 + g*m*(h1) = 1/2*m*(v2)^2 + g*m*(h2)
1/2*m*(v2)^2 = 1/2*m*(v1)^2 - g*m*(h2-h1)
(v2)^2 = (v1)^2 - 2*g*(h2-h1)
v2 = sqrt[ (v1)^2 - 2*g*(h2-h1) ]

-- 
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0}}}box{z-y-.1.1+z}box{-.1.1+x}box{.1z-.1}pigment{rgb<.8.2,1>}}//Jellby

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