A 3-kg block is traveling to the right at 5 m/s, and a 1-kg block is traveling to the left at 3 m/s.

(a) Find the velocity v_cm of the center of mass. 

(b) Subtract v_cm from the velocity of each block to find the velocity of each block in the center-of-mass reference frame. 

(c) After they make an elastic collision, the velocity of each block is reversed in this frame. Find the velocity of each block after an elastic collision. 

(d) Transform back into the original frame by adding v_cm to the velocity of each block. 

(e) Check your result by finding the initial and final kinetic energies of the blocks in the original frame.