Elastic Collision of Identical Masses

Steps:

• Assume head-on collision in one dimension with equal masses m.
• Initial momentum: mv (X) + 0 (Y) = mv total.
• Initial kinetic energy: (1/2)mv².
• For elastic collision, use velocity formulas: post-collision velocity of X is 0, Y is v (from conservation laws).

Why D is correct:

• In an elastic collision of equal masses with one at rest, momentum and kinetic energy conservation dictate the moving object stops and transfers all velocity to the stationary one.

Why the others are wrong:

• A: Both moving right at v doubles momentum to 2mv, violating conservation.
• B: X rebounds at v, Y stationary conserves momentum but not kinetic energy (like inelastic).
• C: X left at v, Y right at v conserves momentum but doubles kinetic energy to mv².

Final answer: D