Two stones, in the form of spheres, fall from a great height through atmosphere. What is the ratio of their momentum, when they attain their...

Momentum is simply the product of mass and velocity (mv). Unfortunately, we don't know the mass or the velocity of either object.

The velocity could be determined through some simple kinematics; for example, we know that the stone spheres are being dropped from an initial velocity of zero, and they are falling through an increasingly thick atmosphere, which will alter the calculation of their terminal velocity as they pass through more and more resistance. Their...

Momentum is simply the product of mass and velocity (mv). Unfortunately, we don't know the mass or the velocity of either object.

The velocity could be determined through some simple kinematics; for example, we know that the stone spheres are being dropped from an initial velocity of zero, and they are falling through an increasingly thick atmosphere, which will alter the calculation of their terminal velocity as they pass through more and more resistance. Their shape also influences their terminal velocity, although a sphere will attain the maximum because the interaction with the medium is as equally distributed as possible.

However, without knowing the mass of the spheres, or the height they drop from, or their diameter, or the time they travel, we cannot know their final momentum. Nevertheless, we can determine that the ratios of their final momentum will be 1:1 - because if both spheres are identical in shape (which was not specified, but if they are not then the problem is impossible to solve) and if both spheres are dropped from the same height at the same time, then according to the basic rules of physics, they should travel at identical velocities for the duration of their fall.