Answer:
Free-fall is defined as the movement where the only force acting on an object is the gravitational force.
By the second Newton's law, we have that:
F = m*a
Where F = Force, m = mass, a = acceleration.
We can write this as:
a = F/m
And the gravitational force can be written as:
F = (G*M/r^2)*m
Where G is the gravitational constant, M is the mass of the Earth in this case, and r is the distance between both objects (the center of the Earth and the free-falling object)
As the radius of the Earth is really big, the term inside the parentheses is almost constant in the region of interest, then we can write:
G*M/r^2 ≈ g
And the gravitational force is:
F = g*m
And by the second Newton's law we had:
a = F/m = (g*m)/m = g
a = g
Then the acceleration does not depend on the mass of the object.
Then the thing that is common among the free-falling objects is the vertical acceleration.
