Final answer:
The ball thrown horizontally experiences greater horizontal displacement than the stone dropped vertically because it has an initial horizontal velocity, while the stone only moves vertically.
Step-by-step explanation:
When a ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically, the object that experiences a greater horizontal displacement after a certain time is the ball thrown horizontally. This is because the stone dropped vertically has no horizontal velocity, so it does not move horizontally. On the other hand, the ball thrown horizontally has an initial horizontal velocity, allowing it to cover a horizontal distance. Since gravity only affects vertical motion, both objects will have the same vertical displacement if they are dropped or thrown at the same time, but the horizontal displacement will be different due to the initial horizontal velocity of the thrown ball.