Conservation of momentum in elastic collision of equal-mass molecules

Steps:

• Resolve post-collision velocities: P has vx = 180 cos 55° (x), vy = 180 sin 55° (y, positive); Q has vx = v cos 34° (x), vy = -v sin 34° (y, negative to balance).
• x-momentum: m × 320 = m (180 cos 55° + v cos 34°).
• y-momentum: 0 = m (180 sin 55° - v sin 34°), so v = 180 (sin 55° / sin 34°) ≈ 180 × (0.8192 / 0.5592) ≈ 264 m/s (≈260 m/s).
• Verify x: 180 cos 55° + 260 cos 34° ≈ 103 + 215 ≈ 318 m/s (matches 320 m/s within rounding).

Why D is correct:

• y-momentum conservation yields v ≈ 260 m/s directly from vector components and equal masses.

Why the others are wrong:

• A: Underestimates speed; fails to account for full y-component transfer.
• B: Possible error from using cos instead of sin ratios or ignoring y-direction.
• C: Equals P's post-speed but ignores momentum balance for Q.

Final answer: D