Final answer:
The acceleration due to gravity is constant for all objects regardless of their mass, therefore, objects of different masses dropped from the same height will hit the ground at the same time. However, the momentum of a twice as massive object hitting the ground will be twice that of a less massive object, due to the direct proportionality of momentum to mass.
Step-by-step explanation:
When two objects of different mass, where one is twice as massive as the other, are dropped from the same height, they will reach the ground simultaneously due to the fact that the acceleration due to gravity is constant for all objects regardless of their mass (as long as there's no significant air resistance). This concept was proven by Galileo and is fundamental to the understanding of physics. The momentum of an object, however, is directly proportional to its mass and velocity. In the case of these two falling objects, where one is twice as massive, the velocity at the point of hitting the ground will be the same for both. Therefore, the momentum of the more massive object will be twice that of the less massive object, because momentum is the product of mass and velocity (p = m*v). So, the object that is twice as massive will hit the ground with twice the momentum.
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