Constructing a Physics Proof: Guidelines & Rules of Thumb

[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.

 

[tiny-tim]

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?

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

 

[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.
s_{y proj} = s_{y obj} when s_{x proj} = s_{x 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.

 

[Jack21222]

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

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.