Objects of different masses hit the ground at the same time when dropped in a vacuum or in a location where air resistance can be neglected. This phenomenon is known as the "equivalence principle" and was famously demonstrated by Galileo Galilei in the late 16th century.
The reason for this can be understood by considering the force acting on an object as it falls. According to Newton's second law of motion, the force acting on an object is equal to its mass multiplied by its acceleration. In the case of a falling object near the surface of the Earth, the force acting on it is the force due to gravity, which is the weight of the object.
The weight of an object is given by the formula: weight = mass × acceleration due to gravity. So, for two objects of different masses, the force due to gravity will be proportional to their masses. However, according to Newton's second law, the force is also related to the object's acceleration.
The key insight is that when an object falls freely under the influence of gravity (with negligible air resistance), both objects experience the same acceleration due to gravity, regardless of their masses. This acceleration is approximately 9.8 meters per second squared (m/s^2) near the surface of the Earth.
Since the acceleration is the same for both objects, their masses cancel out when calculating the force. As a result, both objects experience the same force due to gravity and undergo the same acceleration. Therefore, they will hit the ground at the same time, assuming other factors like air resistance are negligible.
However, it's important to note that in real-world situations where air resistance is not negligible, objects with different masses can experience different air resistance forces. In such cases, the objects may not fall at exactly the same rate.