The first observational measurements on the law of falling bodies were made by Galileo Galilei (1564-1642).
The famous law, considering the distance d traveled during the fall, is:
[1] d = g t² / 2
where g is a constant representing the local gravitational acceleration (on Earth a mean value is g = 9.8 m/s² ), and t is the time elapsed. In more easily observable terms, the fall time can be measured reversing the relationship [1] :
[2] t = √(2d/g) .
Galileo predicted (inspired by what Domingo de Soto had already conceived in 1551) that all bodies follow this law regardless of their mass, studying rolling balls (rather than dropping them from the famous Tower of Pisa). However, everyday experience tells us that light bodies fall more slowly: this is simply due to the friction of the fluid in which they are immersed (e.g., air).
A rather expensive experiment was reported to have been carried out on the Moon, when a hammer and a feather were dropped and touched the ground at the same time (astronaut David Scott on August 2, 1971).
I propose the following more economical experiment: drop a coin that is not too small, for example a 2 euro coin, flat on its face, placing a small piece of paper, e.g. 5 mm in diameter, on top of it. A good height would be half a meter. You can observe that the piece of paper reaches the ground at the same time as the coin, which prevents the air from slowing it down.
You could also place the piece of paper in a transparent container that you then drop, but this would make it less clear to observe.
As a side note, it can be observed that a body in free fall accelerates until this acceleration equals the acceleration of gravity, due to the mass of the body (tipically the Earth) on which it is falling (possibly slowed down by air resistance, known as drag force). Once this is reached, the speed of fall, known as terminal velocity, remains constant. On contrary, a body falling in a vacuum never reaches terminal velocity because there is no drag force; it accelerates indefinitely as long as it is falling.





