In a vacuum, an object's mass does not affect its motion during free fall. This is because the force of gravity acts equally on all objects, regardless of their mass. This is famously demonstrated by Galileo's thought experiment where he proposed that a feather and a cannonball would fall at the same rate in a vacuum.

Here's why:

* Acceleration due to gravity (g): The acceleration due to gravity on Earth is approximately 9.8 m/s². This means that every object, regardless of its mass, falls at the same rate.

* Force of gravity (F): The force of gravity acting on an object is directly proportional to its mass (F = mg). However, this force also affects the object's acceleration, which is inversely proportional to its mass (a = F/m).

* Cancellation: These two factors cancel each other out. The increased force of gravity on a heavier object is precisely counteracted by its larger inertia, resulting in the same acceleration as a lighter object.

However, in reality, air resistance plays a significant role. Air resistance is a force that opposes the motion of an object through the air. The amount of air resistance depends on factors like the object's shape, size, and velocity.

* Effect on lighter objects: Lighter objects experience a greater impact from air resistance relative to their weight, slowing their descent.

* Effect on heavier objects: Heavier objects have a greater weight, which can overcome air resistance more effectively.

Therefore, in the presence of air resistance:

* Lighter objects will fall slower than heavier objects.

* Heavier objects will fall faster than lighter objects.

In conclusion:

* In a vacuum: All objects fall at the same rate, regardless of mass.

* In air: Heavier objects will fall faster than lighter objects due to air resistance.