Final answer:
To calculate the amount of time it takes for the skaters to reach the edge of the rink, we can use the concept of conservation of linear momentum. The initial momentum of each skater is found and the final momentum of the system can be calculated using the law of conservation of momentum. It takes approximately 18.24 seconds for the skaters to reach the edge of the rink.
Step-by-step explanation:
To calculate the amount of time it takes for the skaters to reach the edge of the rink, we can use the concept of conservation of linear momentum. Since the skaters hold onto each other, their total momentum remains constant. We can find the initial momentum of each skater and the final momentum of the system, and then use the law of conservation of momentum to solve for the time it takes to reach the edge of the rink.
Before the collision, the 85.0 kg skater moving north has a momentum of (85.0 kg)(2.45 m/s) in the north direction. The 48.0 kg skater moving west has a momentum of (48.0 kg)(4.45 m/s) in the west direction.
After the collision, the skater holds onto each other, and their total momentum must equal zero since there are no external forces acting on the system. Therefore, we can set up the equation:
initial momentum of north-moving skater + initial momentum of west-moving skater = 0
(85.0 kg)(2.45 m/s) + (48.0 kg)(4.45 m/s) = 0
Solving for the time, we find that it takes approximately 18.24 seconds for the skaters to reach the edge of the rink.