Final answer:
The mass of the second skater, when two figure skaters push off each other and one has a mass of 80 kg with a velocity of 3 m/s and the other a velocity of -5.3 m/s, is calculated at 45.28 kg, which rounds to approximately 45 kg.
Step-by-step explanation:
When two figure skaters push off each other while standing motionless on the rink, they exemplify the conservation of momentum principle in physics. The first skater has a mass of 80 kg and a final velocity of 3 m/s. We are asked to find the mass of the second skater given that her final velocity is -5.3 m/s.
To solve this, we can use the conservation of momentum equation:
Momentum before = Momentum after
The total initial momentum is zero since they are motionless. Thus:
0 = (mass of first skater) × (velocity of first skater) + (mass of second skater) × (velocity of second skater)
0 = (80 kg) × (3 m/s) + (mass of second skater) × (-5.3 m/s)
Solving for the mass of the second skater, we get:
mass of second skater = −((80 kg) × (3 m/s)) / (-5.3 m/s)
mass of second skater = 240 kg−m/s / 5.3 m/s
mass of second skater = 45.28 kg,
which we can round to the nearest whole number, 45 kg.