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I'm doing a practice problem and I thought I had a good solution, but it turns out I'm wrong and I'd like to know exactly why. The book seems to do it in different way, but I don't see why theirs is the right way.

The problem is this:

So, here's the process I tried doing:

-Find what the y component of the package velocity with respect to S1 (S1 is rocket 1's frame), using the velocity addition rule since we have the velocity of S with respect to S1 and the velocity of the package with respect to S

-Find the velocity of rocket 2 with respect to S1, using the velocity addition rule since we have the velocity of S with respect to S1 and the velocity of rocket 2 with respect to S

-Then, to make it so the package hits rocket 2 as it goes across the gap, we set these two velocities equal.

This is where the solution and I seem to disagree, the solution says that the y component of the package velocity and the velocity of rocket 2 should match in frame S, not rocket 1's frame! I guess I don't actually see why one is preferable over the other, but theirs must be right. If I had to guess I'd say it's something involving proper time or proper velocity, but I don't see what exactly.

Any help would be great, thanks!

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# Why doesn't my solution work?

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