Both horizontal accelerations are zero. Both vertical accelerations are equal . . . the acceleration of gravity. They fall for the same length of time. If thrown at the same time, then they hit the ground at the same time. A bullet shot from a high powered rifle and one dropped from the muzzle at the same time hit the ground at the same time.
The accelerations of balls thrown horizontally with different initial velocities are the same due to gravity, and thus, they hit the ground at the same time. The student's experiment would collect times to hit the ground to show that acceleration is independent of the object's velocity. ;
Both balls thrown horizontally will experience the same vertical acceleration due to gravity, meaning they will hit the ground at the same time. Their horizontal motions do not affect the time it takes for them to fall. Thus, regardless of the difference in initial speeds, they land simultaneously.
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