There is a very simple equation for an inelastic collision but it really only applies to 2d scenarios:

$$v = \frac{(m_1 u_1 + m_2 u_2)}{(m_1+m_2)}$$

What would be the equation for an inelastic collision in a 3d environment?

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    $\begingroup$ The equation you wrote has nothing special to do with inelastic collision. It is simply the center-of-mass velocity, and in 3D it looks the same except that $v$, $u_1$ and $u_2$ are 3D vectors. $\endgroup$ – Sofia Mar 8 '15 at 12:27

Short answer: Same thing.

Longer answer: recall that both momentum ($p$) and velocity ($v$) are both vectors. You're used to vectors in one or, at most, two dimensions but we can expand the vector space into arbitrarily many dimensions so that your vector $p$ would have components $(p_1, p_2, ... , p_n)$ for $n$ linearly independent components. For a three dimensional collision problem you would just have $(p_x, p_y, p_z)$ for each momentum vector and $(v_x, v_y, v_z)$ for each velocity vector. Just like in two dimensional collision problem, each component $x$, $y$, and additionally in this case, $z$ of the total momentum is conserved.


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