Deriving the inelastic collision equation

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GreenSabbath
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http://upload.wikimedia.org/math/a/8/a/a8a9e87d40533ad47fadb40725a4a3e5.png"

How wxactly has this equation be derived?

http://upload.wikimedia.org/math/3/c/5/3c53f3d1c66725053decc7e3e546c32d.png"

Can someone help me with the derivation. I can't trace the orgin of the second part od the systems of equation.

Help needed urgently Thanks
 
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When talking about certain physical problems, you should consider the assumptions under which some equations related to these problems are derived. For example, what is conserved in every collision?

Further on, this link should help: http://hyperphysics.phy-astr.gsu.edu/hbase/inecol.html" .
 
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