Relative velocity conservation in elastic collisions

Steps:

• Initial velocity of X: 6 cm/s towards Y; velocity of Y: 0 cm/s.
• For perfectly elastic collision, magnitude of relative velocity after equals magnitude before, but direction reverses.
• Initial relative velocity (approach): 6 cm/s - 0 cm/s = 6 cm/s.
• Post-collision relative velocity (separation): v_Y - 2 cm/s = 6 cm/s, so v_Y = 8 cm/s.

Why D is correct:

• Follows the elastic collision rule that relative velocity reverses, giving v_Y = v_X + initial relative speed.

Why the others are wrong:

• A: Relative velocity would be 0 cm/s, violating elastic separation.
• B: Assumes equal masses (v_Y = 4 cm/s if X stops), but X continues at 2 cm/s.
• C: Implies X rebounds or stops, but it moves forward at 2 cm/s.

Final answer: D