Why do two objects big or small fall at the same velocity?

Two falling objects, regardless of their mass, will not necessarily fall at the exact same velocity. In the absence of air resistance, all objects will accelerate due to gravity at a rate of approximately 9.8 meters per second squared (32 feet per second squared). However, the presence of air resistance, also known as drag, will cause the velocity of falling objects to vary depending on their size, shape, and other factors.

The effects of air resistance are more significant for smaller objects with a larger surface area relative to their mass compared to larger objects with a smaller surface area relative to their mass. This is because the drag force is proportional to the surface area of the object and the velocity of the airflow around it. Smaller objects, such as a feather, will experience a greater air resistance compared to larger objects, such as a bowling ball. As a result, the smaller object will fall slower than the larger object.

In real-world conditions, the acceleration due to gravity is modified by the drag force, resulting in a lower observed acceleration. The rate at which an object's velocity increases due to gravity and decreases due to drag will determine its "terminal velocity," the constant velocity at which the drag force balances the gravitational force.

In the famous experiment conducted by Galileo Galilei in the 16th century, two objects of different masses were dropped simultaneously from the Leaning Tower of Pisa. While both objects reached the ground at roughly the same time, Galileo noted that the heavier object did so slightly faster. However, this observation was not due to the mass of the objects alone, but rather a combination of mass, shape, and air resistance.

Therefore, while it is commonly stated that two objects fall at the same velocity due to gravity, this is true only in a theoretical vacuum where air resistance is absent. In the presence of air, objects experience a drag force that affects their velocity and causes smaller objects to fall slower than larger objects.