Final answer:
Ignoring air resistance, both the horizontally thrown ball and the dropped ball will hit the ground at the same time because vertical motion is independent of horizontal motion and both are subject to the same gravitational acceleration.
Step-by-step explanation:
If we ignore air resistance, two identical balls thrown from the same height off a cliff, with one thrown horizontally and the other dropped, will hit the ground at the same time. The reason behind this is that gravitational acceleration is the same for both balls and acts only in the vertical direction.
The horizontal throw adds a horizontal velocity component, but this doesn't affect the time it takes for the balls to fall, because gravity doesn't influence the horizontal motion. Hence, the vertical descent is independent of horizontal velocity. Thus, both the horizontally thrown ball and the dropped ball will experience the same gravitational pull downward and will hit the ground simultaneously, assuming ideal conditions without air resistance.