Elastic collision: conserve momentum and reverse relative velocity

Steps:

• Conservation of momentum: initial total mu (2m at +u, m at -u), so 2v₁ + v₂ = u.
• Elastic condition: relative velocity reverses, v₂ - v₁ = - (u₂ - u₁) = 2u.
• Solve: v₂ = v₁ + 2u; substitute into momentum: 2v₁ + v₁ + 2u = u → 3v₁ = -u → v₁ = -u/3.
• Then v₂ = -u/3 + 2u = 5u/3 (2m rebounds left at u/3, m forward right at 5u/3).

Why A is correct:

• Velocities match elastic formulas: v₁ = (m₁ - m₂)/(m₁ + m₂) u₁ + 2m₂ u₂ /(m₁ + m₂) yields -u/3 and 5u/3.

Why the others are wrong:

• B: Post-collision momentum 2m(-u/6) + m(2u/3) = mu/3 ≠ mu (violates momentum conservation).
• C: Relative velocity 2u - (-u/2) = 5u/2 ≠ 2u (violates elastic reversal).
• D: Post-collision momentum 2m(-u) + m(2u) = 0 ≠ mu (violates momentum conservation).

Final answer: A