I understand that momentum is conserved in this problem, but can anyone explain to me how kinetic energy is conserved as well? The answer says that it's an elastic collision
Apply momentum and energy conservation equations.
If you get an identity equation (i.e. v = v, 4/3 = 4/3), it's elastic, which it is in this case.
If you get an inequality, it will be inelastic.
Calculate total momenta of the system. Define the mass of Ball 1 to be 2m, mass of Ball 2 to be m. Total momenta is 2m*v=2mv. Ball 1 is now moving at 1/3 *v. Its momenta is 2m*v/3=2mv/3. The momenta of Ball 2 is therefore mv (2-2/3)=mv(4/3).
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