Final answer:
In a tug of war on ice, when James pulled on the rope and moved 6 m towards the midpoint, conservation of momentum dictates that Ramon also moved 6 m in the opposite direction, towards the center.
Step-by-step explanation:
The question is related to the conservation of momentum in a system of two people on ice, where friction is negligible. When James, who has a mass of 90 kg, pulls on the rope and moves 6 m closer to the midpoint, this is because both James and Ramon are exerting forces on each other through the rope.
Since the total momentum of the system must be conserved (the initial total momentum is zero as both are initially stationary), the distance Ramon moves must comply with this principle.
Let's calculate Ramon's distance covered.
If James moves 6 m toward the midpoint, then combined, they must cover 6 m on one side and Ramon must cover an equal distance, in this case, another 6 m, on his side, such that the center of mass of the system does not change its position.
Therefore, in this tug of war, Ramon will move in the opposite direction to James, covering a distance of 6 m toward the center.