Having worked it out myself last night, I realized that problem 9 is a bit more ... punishing than it really ought to be. The physics is easy, but the integral you need to solve is somewhat pathalogical.
Thus, the MASSIVE HINT, which sets up the integral for you and gives you the basic result. Note that I said "Use any means necessary to evaluate the integral required." This means you can look it up, perhaps with the Wolfram Integrator.
If you read the hint carefully, there are bonus points for solving the thing the hard way, and further bonus points for proving that it reduces to our usual expression for small heights.
Further hint: don't reinvent the wheel. What are the odds I made this problem up, and what are the odds that it comes from any number of advanced mechanics books?
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