Only scenario 1 (both move 3m) and scenario 4 (A moves 1.5m and B moves 4.5m) satisfy the principle of conservation of momentum and are possible scenarios.
How to find distance?
To solve this problem, we need to consider the principle of conservation of momentum. Since the skaters are initially at rest and no external forces act on them, the total momentum before the pulling is zero and must remain zero after the pulling.
To analyze each scenario:
1. Both move 3m:
Assume they both move towards each other.
Initial total momentum = 0 (both are at rest).
Final momentum after moving 3m
(50 kg × 3 m/s) + (70 kg × -3 m/s) = 0 (momentum is conserved).
This scenario satisfies the conservation of momentum as the product of mass and velocity for both skaters is equal and opposite. They will indeed meet after moving 3m each.
2. A moves 2.5m, and B moves 3.5m:
Following the same logic as above, the final momentum should be 0.
(50 kg × 2.5 m/s) + (70 kg × -3.5 m/s) = -125 kg m/s.
This violates the conservation of momentum as the total momentum is not zero. Therefore, this scenario is not possible.
3. A moves 3.5m, and B moves 2.5m:
Similar calculations lead to a final momentum of 125 kg m/s, again violating the conservation of momentum. This scenario is also not possible.
4. A moves 1.5m, and B moves 4.5m:
Applying the conservation principle: (50 kg × 1.5 m/s) + (70 kg × -4.5 m/s) = 0.
This scenario satisfies the conservation of momentum as the total momentum remains zero. Therefore, this is a possible scenario where A moves 1.5m and B moves 4.5m before they meet.
Therefore, only scenario 1 (both move 3m) and scenario 4 (A moves 1.5m and B moves 4.5m) satisfy the principle of conservation of momentum and are possible scenarios.