Final answer:
When a ball is dropped, it accelerates downwards due to gravity at a constant rate, and if there's no air resistance, its vertical motion is independent of any horizontal motion. Even a ball thrown horizontally is in a state of free fall. Hence, the ball returns with the speed it had when it left, under ideal conditions without air resistance.
Step-by-step explanation:
When you drop a ball, assuming there is no air resistance, the vertical motion of the ball is influenced only by gravity. The acceleration of the ball is downwards, due to gravity, at approximately 9.81 m/s2 on Earth, regardless of any horizontal motion it might have. This implies that a ball dropped from rest and a ball thrown horizontally will hit the ground at the same time if dropped from the same height. The horizontal motion of the ball, when thrown, does not influence the vertical acceleration. Therefore, while the horizontal velocity is constant, the vertical velocity increases linearly over time due to the constant acceleration due to gravity.
For a ball that is thrown as well as dropped, they will both experience free fall. This term refers to any motion of a body where gravity is the only force acting upon it. Even a ball thrown horizontally is in a state of free fall, and therefore, the ball returns to the ground with the speed it had when it left, assuming no other forces are acting upon it.