Well… I hope you can answer question (c) without doing any calculations whatsoever.

And, although you say that this was posed as a Mathematica problem, basically all of it can be done very quickly with a pen and paper and no digital help at all.

As much as I love and promote Mathematica, the greatest insight sometimes is gained by simply doing a calculation by hand. Using Mathematica for this problem is kind of like using high explosives to open up a jar of pickles.

And this sort of highlights some of the aspects of the debate around the question of using computer-based mathematics in place of hand calculations. Sometimes the focus on writing the computer code can divert one from pointing one's focus at gaining physical insight. So, take this just as a reminder that you should think about the physics first, whether or not you are doing your calculations by hand or with the help of a tool like Mathematica.