In the event of a ball being dropped and a second ball being thrown downwards, which condition is necessary for both to hit the ground simultaneously?

For both balls, whether one is dropped and the other is thrown downwards, to hit the ground at the same time, the key factor is that they experience the same acceleration due to gravity. This acceleration is approximately 9.81 m/s² near the surface of the Earth, and it acts equally on all objects regardless of their mass.

When the first ball is simply dropped, it starts with an initial velocity of zero and accelerates downward solely due to gravity. The second ball, thrown downwards, will also experience this same acceleration, which influences its motion. If both balls are released or thrown from the same height, their differing initial velocities and the uniform acceleration due to gravity will determine when they hit the ground.

If the acceleration due to gravity were different, it would affect the time each ball takes to reach the ground, potentially causing them to hit at different times even if they started from the same height. Therefore, ensuring that the acceleration due to gravity is equal is crucial for both balls to hit the ground simultaneously.