Conservation of momentum in the perpendicular direction

Steps:

• Initial momentum perpendicular to the initial path is zero for both objects.
• After collision, X's perpendicular velocity component is 2.0 × sin 41° ≈ 1.31 m/s.
• Y's perpendicular velocity component is v × sin 60° ≈ v × 0.866 in the opposite direction.
• Momentum conservation requires the perpendicular velocity components to balance in magnitude: v × sin 60° = 2.0 × sin 41°.
• Solve for v: v = 2.0 × (sin 41° / sin 60°) ≈ 2.0 × 0.757 ≈ 1.5 m/s.

Why C is correct:

• It matches the calculation from balancing perpendicular velocity components using the conservation of momentum law, where y-momenta sum to zero.

Why the others are wrong:

• A: Too low; underestimates the ratio of sines (0.656/0.866 ≈ 0.757, times 2.0 gives 1.5, not 0.8).
• B: Too low; ignores the full sine ratio, yielding ~1.2 instead of 1.5.
• D: Too high; overestimates by adding extra factors not in the perpendicular balance.

Final answer: C