- #1

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My attempts:

The speed of the masses relative to the ground will be v+u and v-u. Considering only the second boat and applying conservation of momentum, you get: Pv = (P - 2P1)(v2) + P1(v + u) + P1(v - u), and v2 = v. That part is fine.

Now considering all the boats in the initial, final, and intermediate stage: 3Pv = (P+P1)v1 + (P+P1)v3 + (P-2P1)v = 2Pv + (P-2P1)(v) + P(v+u) + P1(v-u). Now the expressions for v1 and v3 as given in the solutions section should not contain v1 or v3, and they must contain u. I don't understand how that's possible since if you simplify the rightmost side of the equation, u is eliminated.