This is a great example of a problem where knowing all the equations in the world won't help you solve the problem, if you don't also think about the Physics of the situation. I mean this one very seriously. Indulge me one more time and write down what you think the point of going through all this math, without the math, is. If you're scoring yourself, give yourself credit for whatever you wrote down. But here is how I would put it.
Mathematical equations represent reality.
This indirect sort of approach turns out to be a very powerful, very rich way of solving all kinds of problems which would be next to impossible otherwise. Math can never represent reality fully. And even when it gives the right answer, if you don't understand the Physics behind the problem, you haven't really learned anything useful or interesting. And the key to that fun is never abandoning your common sense. After you have gone through all of the above, you may find it worthwhile to actually work through the numbers and confirm that you get what you expected.