When two objects with different weights are dropped from the same height simultaneously, they will indeed hit the ground at the same time, neglecting the effects of air resistance. This phenomenon can be explained by the principles of free fall and acceleration due to gravity.
In the absence of air resistance, all objects near the Earth's surface experience the same acceleration due to gravity, which is approximately 9.8 meters per second squared (m/s²). This acceleration is constant and acts on all objects regardless of their mass.
According to the laws of physics, when an object is in free fall near the Earth's surface, its velocity increases at a constant rate due to gravity. This means that the speed at which an object falls, regardless of its mass, will continue to increase as it falls.
When two objects are dropped together, the heavier object does indeed experience a greater force due to its greater mass. As a result, it will accelerate at a faster rate than the lighter object. However, since both objects start from rest, they will have the same initial velocity.
Due to the constant acceleration, both objects will gain velocity at the same rate as they fall. This means that the time it takes for both objects to hit the ground will be the same. The heavier object will be moving faster than the lighter one, but they will cover the same distance in the same amount of time.
It's important to note that this explanation assumes the absence of air resistance, which can affect the motion of objects in real-world scenarios. In reality, if the objects have significantly different surface areas or shapes, air resistance could come into play and affect their motion. However, in a vacuum or if the objects are dense and streamlined, the effect of air resistance can be minimized.