Answer:
To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the interaction is equal to the total momentum after the interaction.
Let's denote the mass of the 60-kg skater as m1 and the mass of the other skater as m2. The initial momentum is zero since both skaters are at rest initially.
Initial momentum = 0
After the interaction, the 60-kg skater acquires a speed of 0.70 m/s. The momentum of the 60-kg skater can be calculated as:
Momentum of the 60-kg skater (m1) = mass (m1) × velocity (0.70 m/s)
The other skater has a speed of 0.88 m/s. The momentum of the other skater (m2) can be calculated as:
Momentum of the other skater (m2) = mass (m2) × velocity (0.88 m/s)
According to the principle of conservation of momentum:
Initial momentum = Final momentum
0 = Momentum of the 60-kg skater (m1) + Momentum of the other skater (m2)
Since we know the momentum of the 60-kg skater (m1) and the velocity of the other skater, we can solve for the mass of the other skater (m2):
0 = m1 × 0.70 m/s + m2 × 0.88 m/s
0 = 60 kg × 0.70 m/s + m2 × 0.88 m/s
0 = 42 kg·m/s + 0.88 m/s × m2
Solving for m2:
-42 kg·m/s = 0.88 m/s × m2
m2 = -42 kg·m/s / 0.88 m/s
m2 ≈ -47.73 kg
The negative value obtained for m2 suggests that there may be an error in the calculations or in the given values. Please double-check the values provided in the problem to ensure accuracy.