Two skaters one with mass 65 kg and the other with mass 43 k

Two skaters, one with mass 65 kg and the other with mass 43 kg, stand on an ice rink holding a pole of length 10 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 43 kg skater move?

Solution

Since the center of mass of the two-skater system does not move, the two skaters will meet at the center of mass of the system. If we let the origin be at the initial position of the 40 kg skater, we can calculate the position of the center of mass. This is also the distance the 40 kg skater will move.

x_cm={43*0+65*10}/(43+65) =6.0185m