✔ 最佳答案
The system consists of three masses, astronaut A, astronaut B, and th toolbox.
Initially, the toolbox is with astronaut A, forming a combined object with mass (60+30) kg, with velocity 1 m/s. The momentum of which is (60+30) x 1 Ns
The momentum of astronaut B is 60 x (-1) Ns, since astronaut B moves towards astronaut A.
Hence, total initial momentum of the system = [(60+30)(1) + 60(-1)] Ns
After astronaut B has got hold of the toolbox, in order to avoid a collision, the final velocity of astonaut A must at least equal to the final velocity of astronaut B, both with the same magnitude and travelling in the same direction. The reason is apparent. If the velocity of A is higher than that of B, A will catch up with B eventually and a collision will occur. On the contrary, if velocity of A is lower than that of B, the final velocity of the toolbox is NOT a minimum.
Therefore, if v is the final velocity of the toolbox, which is in the hand of astronaut B, the velocity of B also equals to v. For a minimum velocity of the toolbox, with reason given above, the final velocity of A equals to v.
Hence, the final momentum of A = 60v
The final momentum of B and toolbox together = (60+30)v
Total final momentum of the system = 60v + (60+30)v
Then, using conservation of momentum,
[(60+30)(1) + 60(-1)] = 60v + (60+30)v
solve for v
