Answer:
The 60 kg skater is traveling at 2.63 m/s in the opposite direction from the 45 kg skater.
Explanation:
The velocity of the 60 kg skater can be found by conservation of linear momentum:
[tex]P_{i} = P_{f}[/tex]
[tex]m_{a}v_{i_{a}} + m_{b}v_{i_{b}} = m_{a}v_{f_{a}} + m_{b}v_{f_{b}}[/tex] (1)
Where:
[tex]m_{a}[/tex]: is the mass of the first skater = 45 kg
[tex]m_{b}[/tex]: is the mass of the second skater = 60 kg
[tex]v_{i_{a}}[/tex]: is the initial speed of the first skater = 0 (he is standing still)
[tex]v_{i_{b}}[/tex]: is the initial speed of the second skater = 0 (he is standing still)
[tex]v_{f_{a}}[/tex]: is the final speed of the first skater = 3.5 m/s
[tex]v_{f_{b}}[/tex]: is the final speed of the second skater =?
By replacing the above values into equation (1) and solving for [tex]v_{f_{b}}[/tex] we have:
[tex]0 = m_{a}v_{f_{a}} + m_{b}v_{f_{b}}[/tex]
[tex]v_{f_{b}} = \frac{-m_{a}v_{f_{a}}}{m_{b}} = \frac{-45 kg*3.5 m/s}{60 kg} = -2.63 m/s[/tex]
The minus sign is because the 60 kg skater is moving in the opposite direction from the other skater.
Therefore, the 60 kg skater is traveling at 2.63 m/s in the opposite direction from the 45 kg skater.
I hope it helps you!
