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Scattering problem: Finding the speed of the scatterer after collision

A particle of mass $M$ moving in a straight line with speed $v$ collides with a stationary particle of the same mass. In the center of mass coordinate system, the first particle is deflected by 90 ...
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Scattering problem: Converting the two-body lab frame problem into a one-body center-of-mass frame problem

I'm reading the section on scattering in Goldstein's Classical Mechanics, and I have a rather basic question about this. It says that scattering in the laboratory is a two-body problem because of ...