When it comes to the "plug and chug" questions, I believe I did well on the first exam of the year, but a large chunk of the grade was creating a proof, and I struggled on that one. It had to do with firing a projectile at an object that is dropped at the same time the projectile is fired.

In my response, I either proved what I was supposed to, or I proved nothing at all. The worst part was I spent a good 45 minutes just solving for each of the variables in terms of the other variables, and was almost using trial-and-error to substitute variables to make things cancel.

So, my question is a general one: Are there any guidelines or rules of thumb to making a sensible proof? Any helpful hints of what steps I should take when presented with a proof?

Sorry I'm not more specific in my question. I know so little about proofs that I don't even know what I don't know. All I do know is I felt completely lost on that exam question, and I resorted to what felt like ad hoc cheap tricks to make equations fit.