# Constructing a proof

1. Mar 9, 2009

### Jack21222

I hope I'm placing this in the right forum. This isn't a question about a specific problem, but rather a general question about constructing a proof as it relates to my first semester physics class.

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.

2. Mar 9, 2009

### tiny-tim

Hi Jack21222!

If the projectile was dropped from rest, then I think you just aim and fire … gravity does the rest.

If you spent 45 minutes, you probably had the wrong equations … they usually set exam questions that come out fairly easily and quickly …

the only general tip I can think of is, if it takes too long, then you're probably doing it wrong, so either

i] scrap what you've done, get a new piece of paper, and start afresh, or
ii] do a different question

3. Mar 9, 2009

### thepopasmurf

My general tip for proving these sort of questions is to try and think of the final equation which the proof is for. For example, with the projectile and falling object, I assume that the proof is that if the projectile would hit the object without gravity then it would with gravity. The equation that comes to mind when I think of that situation is that when the x values of the objects are the same, the y values are also the same.
sy proj = sy obj when sx proj = sx obj
Then solve with relevant equations.

If the final equation is already given, I dunno, think of relevant equations, find the variables that link the equations to the final equation.
Practice helps a lot for these kind of questions as well.

4. Mar 9, 2009

### Jack21222

Thanks for the responses.

First, he gave us 2 hours to solve 5 problems, so I don't think they were meant to come out that quick or easy.

Second, I know that "gravity does the rest," but I was struggling to put that into a mathematic proof.

In the end, I did what thepopasmurf suggested and tried proving that the y positions are the same when the distance between them is zero. I solved for time in the x-displacement formula in terms of x, then substituted that in for the t in the y-displacement formulas for the projectile and dropped object. I then set them equal to one another.

The "cheap trick" I used was then setting x, representing the distance between them in the x-direction to 0. When I do that, the y position of the projectile and dropped object are the same... But it also makes everything 0, so I may have proven nothing at all.

I also resorted to making the initial height of the projectile 0, by making that my origin, just to get rid of that irrelevant variable. I hope that is allowed.

I guess I just need more practice. I appreciate that the professor doesn't want us to get used to a slew of plug and chug problems, and wants us to think in terms of proofs and derivations, but it's tough, especially when it's 20% of our grade.