The hardest-hit home run?

We present a problem to be assigned or done as an in-class activity in an upper-division undergraduate course on computational physics. The problem involves a home run hit by Mickey Mantle on May 22, 1963, which he famously called ``the hardest ball I ever hit''. Is this home run truly one for the record books, or has it been eclipsed by players in the modern era? Modeling the trajectory of a baseball involves consideration of both wind resistance and the Magnus effect, and is an interesting application of numerical solution of ordinary differential equations. Ultimately, the answer is that Mantle would compare favorably to the most powerful batters currently playing, but to arrive at that conclusion we must reflect on the plausibility of results and sources of uncertainty.