The 2 skaters, one with a mass of 80 kg and the other with a mass of 50 kg, are facing each other and push off each other. As a result of this interaction, the 50 kg skater moves eastward with a velocity of 5 m/s.
To understand this scenario, we can use the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant if no external forces act on it. In this case, the skaters are the system.
The momentum of an object is calculated by multiplying its mass by its velocity. So, the momentum of the 50 kg skater before the interaction is given by:
Momentum1 = mass1 * velocity1
After the interaction, the 50 kg skater moves eastward with a velocity of 5 m/s. The momentum of the 50 kg skater after the interaction is given by:
Momentum2 = mass2 * velocity2
Since no external forces act on the system, the total momentum before the interaction is equal to the total momentum after the interaction:
Momentum1 + Momentum2 = Momentum1' + Momentum2'
Given that the 50 kg skater moves eastward with a velocity of 5 m/s after the interaction, we can substitute the values into the equation:
mass1 * velocity1 + mass2 * velocity2 = mass1 * velocity1' + mass2 * velocity2'
We can now plug in the values:
80 kg * 0 m/s + 50 kg * 0 m/s = 80 kg * velocity1' + 50 kg * 5 m/s
Simplifying the equation gives us:
0 = 80 kg * velocity1' + 250 kg * m/s
To find the velocity of the 80 kg skater, we need to solve for velocity1':
80 kg * velocity1' = -250 kg * m/s
velocity1' = (-250 kg * m/s) / 80 kg
velocity1' ≈ -3.125 m/s
Therefore, the 80 kg skater moves westward with a velocity of approximately 3.125 m/s after the interaction.