Final answer:
To determine how long it will take the skaters to glide to the edge of the rink, we apply the conservation of momentum for their combined mass, calculate their resultant velocity after the collision, and then calculate the time to reach the rink's edge using the radius of the rink divided by their resultant speed.
Step-by-step explanation:
The question revolves around the application of the conservation of momentum and the principles of circular motion in a frictionless environment. When the 70.4 kg skater going north at 2.54 m/s collides with the 56.0 kg skater who was heading west at 4.75 m/s, their combined center of mass will move in a direction according to the resultant vector from their momenta. To find the time it takes for them to reach the edge of the ice rink, one must calculate their resultant speed and then use the radius of the rink to determine the time taken for their trajectory to intercept the edge of the rink.
Since the situation involves a conservation of momentum in a closed system, we need the combined mass, the components of the initial velocities, and the resultant velocity after collision to solve the problem. The travel time to the edge of the rink is then found by dividing the radius by the resultant speed, assuming that the skaters continue to move at a constant speed along a straight line from the center to the edge of the rink.