Final answer:
Based on the law of conservation of momentum and assuming no external forces, the velocity of the mixed-pair ice skaters after they meet is zero, because they started from rest and the total momentum must remain constant.
Step-by-step explanation:
When considering the scenario where two skaters, a man and a woman, standing motionless on ice suddenly pull each other closer using only their arms, we apply the law of conservation of momentum to determine their resulting velocity after they meet. Since there is no friction between the skates and the ice, the total momentum of the system must remain constant. Initially, because both skaters are motionless, the total momentum is zero. As they pull each other closer, they will move towards each other with opposite velocities that are equal in magnitude due to their masses being the same and the principle of action-reaction forces. Once they meet, their velocities will be such that when combined (since they are now connected), the total momentum of the system is still zero.
Therefore, their velocity with respect to the ice after their bodies have met is zero. This conclusion is based on the assumption of no external forces acting on the system, and it exemplifies the conservation of momentum where the velocity of one skater is equal and opposite to that of the other, resulting in no net movement of the center of mass of the system.