Question

Two skaters, one with mass 55 kg and the other with mass 50 kg, stand on an ice rink holding a pole of length 5 m and negligible mass. Starting from the ends of the pole, the skaters pull themselves along the pole until they meet. How far does the 50 kg skater move?

Answer 1

The 50 kg skater moves 2.62 meters

Step-by-step explanation:

As they pull themselves forward, both skaters will meet at the center of mass of the system. If we set the origin at the 50 kg skater's starting position, that skater's displacement will be equal to the center of mass. The center of mass can be determined as:

`x_(cm) = (m_(1)x_(1)+ m_(2)x_(2) )/(m_(1)+m_(2))`

Let's assume index 1 for the 50 kg skater and index 2 for the 55 kg skater. Since the origin is at skater 1 starting position, x1 = 0 and x2 = pole length = 5 m, yielding the following:

`x_(cm) = (55*5)/(50+55)= 2.62`

Therefore, the 50 kg skater moves 2.62 meters