This question currently has a bounty on it and is receiving a lot of attention. But to me it looks like a question that is normally closed for being off-topic. The question reads like a homework problem, and there appears to be little effort from the OP other than stating a method they tried to use that did not work for them. The question is asking how to solve the problem rather than asking about understanding a physics concept.
Additionally, many of the answers appear to be complete or nearly complete solutions to the problem. Even if the question is acceptable, why are these answers acceptable? I thought complete solutions to problems like these were not supposed to be posted as answers. I did attempt to flag some of the answers as solutions, and I received back:
With a score of +9 and no close votes, it seems pretty clear the community does not consider this an off-topic homework question.
But why does the fact that it has not been considered an off-topic homework question mean that posting full solutions is fine? They seem to be two separate policies. The bounty did call for actual solutions, so is it fine to go against usual policy if you put a bounty on the question?
I understand that it is a very interesting problem whose solution is not straight-forward, but it still seems like it should be considered off-topic. Is this just an instance where the community has decided to forgo the usual rules and tackle an interesting problem? What makes this problem different from other homework problems to make it acceptable?