1. The problem statement, all variables and given/known data Two spheres of equal radius and masses 5.00 kg and 15.0 kg are sliding towards each other along the same straight line across a frictionless, horizontal surface. Vi1 = 15.0 m/s and Vi2= -9.00 m/s, respectively. During the collision, 25% of the total initial kinetic energy is lost...use the results above to find the final velocities of the two objects in the center of mass reference frame. 2. Relevant equations Kf = 1/2 m1 v1f ^2 + 1/2 m2 v2f ^2 Kf = 1/2 M Vcm ^2 + 1/2 m1 u1f ^2 + 1/2 m2 u2f^2 m1 u1f + m2 u2f = 0 3. The attempt at a solution This was a multi-step problem in which my professor gave us the above equations. I already solved for Vcm, which is -3.0 m/s. This would give sphere 1 a ui of -12.0 m/s and sphere 2 a ui of 12.0 m/s. I calculated Ki to be 1170 Joules, and calculated the value of Kf to be 75% of the value, or 877.5 Joules. However, I am unsure as to how to use the above equations in order to solve for uf and vf, since there is a change in kinetic energy. I tried several things, like plugging in random numbers, solving for one of the variables and plugging it back in, and have so far been stumped. Please help!