Conservation of mechanical energy equates final speeds

Steps:

• Both coins start with identical initial kinetic energy (1/2)mu² from speed u and same potential energy at table height h.
• Both end at ground level, so identical decrease in potential energy mgh.
• Negligible air resistance conserves mechanical energy, yielding equal final kinetic energies.
• Equal final kinetic energies mean equal final speeds regardless of trajectory.

Why A is correct:

• Conservation of energy law ensures final speed equals initial speed for horizontal projection (X) and sqrt(u² - 2gh + (u sinθ)² adjusted for fall) for Y, but nets to u for both due to symmetric energy balance.

Why the others are wrong:

• B: Coin Y travels greater vertical distance, rising extra height (u sin30°/g) before falling total h plus twice that rise.
• C: Both experience identical vertical acceleration g downward.
• D: Horizontal speeds differ; X retains u, Y retains only u cos30° = u/√2.

Final answer: A