Two figure skaters who pushed off each other move at the same speed if
A. They push with the same force.
B. The ice does not cause any friction.
C. They have the same mass.
D. There is no air resistance.
The correct answer is C. They have the same mass.
According to Newton's third law of motion, when two objects interact, they exert equal and opposite forces on each other. In this case, when the two figure skaters push off each other, they exert equal and opposite forces on each other. Since the forces are equal, according to Newton's second law of motion (F=ma), the acceleration experienced by both skaters will be the same.
If they have the same mass, and since acceleration is determined by dividing the force by the mass, the acceleration will be the same for both skaters. If the initial speeds of the skaters are the same, then they will continue moving at the same speed after pushing off each other.
The other options (A, B, and D) do not guarantee that the skaters will move at the same speed. If the skaters push with different forces, experience friction from the ice, or face air resistance, it will affect their speeds and they will not move at the same speed.