How does the speed of a dropped object change with height according to classical mechanics?

In classical mechanics, when an object is dropped, it accelerates due to the force of gravity. As it falls toward the ground, the object's speed increases. The fundamental principle at work is that the acceleration caused by gravity (approximately 9.81 m/s² near the Earth's surface) remains constant regardless of the object's height. As the object falls from a greater height, it has more time to accelerate, thus resulting in a higher speed upon reaching a specified point.

When the object is released, it starts from rest and gains speed as it falls, leading to an increase in velocity. The relationship between height and speed can also be analyzed mathematically using the equations of motion. Specifically, the speed of the object just before it hits the ground can be calculated using the potential energy (which is related to height) being converted into kinetic energy (which relates to speed). Thus, the greater the height from which the object is dropped, the greater its final speed will be just before it impacts the ground.