Elastic collision formulas for 1D head-on collision

Steps:

• Assign directions: v_{Pi} = +1.2 m/s (right), v_{Qi} = -1.0 m/s (left).
• Apply momentum conservation: m_P v_{Pi} + m_Q v_{Qi} = 0 = m_P v_{Pf} + m_Q v_{Qf}.
• Apply elastic condition: v_{Qf} - v_{Pf} = v_{Pi} - v_{Qi} = 2.2 m/s.
• Solve: v_{Pf} = -1.2 m/s, v_{Qf} = 1.0 m/s; speeds = 1.2 m/s (P), 1.0 m/s (Q).

Why C is correct:

• Not enough information.

Why the others are wrong:

• A: Does not conserve kinetic energy (final KE = 0.48 J < 0.66 J).
• B: Violates momentum conservation (final momentum ≈ 1.42 kg·m/s ≠ 0).
• D: Violates momentum conservation (final momentum ≈ 2.14 kg·m/s ≠ 0).

Final answer: Not enough information.