Independence of horizontal and vertical motion in projectile motion

Steps:

• Both balls fall from the same height with zero initial vertical velocity, so vertical motion is identical: time to ground $t = \sqrt{2h/g}$, same for both.
• Horizontal velocity is constant (no air resistance): first ball at 20 m/s, second at 10 m/s.
• Horizontal distance = velocity × time, so first ball travels $20t$, second $10t$: distances different.
• Landing times are the same due to matching vertical fall.

Why C is correct:

• Vertical motion determines time identically; horizontal motion determines distance proportionally to initial speed (projectile motion independence).

Why the others are wrong:

• A: Distances differ due to different horizontal speeds.
• B: Times are the same from identical vertical drops.
• D: Times are the same, not different.

Final answer: C