How to think about physics? / How to approach a difficult problem?

[azukibean]

How I currently approach a difficult problem:
-draw a diagram
-list out all the given variables and "solve-for" variable
--use variables to match to a formula ("oh they didn't give the time, I should use the formula V^2-V0^2 = 2*a*(S-S0)," or "I have a, t, and V0, and assuming S0 is 0, I can use S = a/2*t^2 + V0*t +S0)
--if I have two unknown variables, I think whether or not I could relate one of those variables in terms of the other

You obviously have a different mindset for maths than for analyzing literature. How to I become better at thinking about physics?
Sometimes how things relate don't jump out at me. And are there better ways to approach a problem?

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ex:

Homework Statement

A student drops her textbook from the top of a roof. It passed a distance of 1.4 m in .02 s (from the top of a window to the bottom). Find the distance from the top of the window to the top of the roof.

Homework Equations

1. v = a*t + v0
2. S - S0 = Vbar*t
3. S = a/2*t^2 + V0*t + S0
4. V^2-V0^2 = 2*a*(S-S0)

The Attempt at a Solution

Thought process:
"I have S, t, and a. I should find the velocity. I use equation 3 and make sure whatever I put in is consistent/makes sense. (-1.4 = (-5)(.02)^2 + 0t + S0 is not consistent, because I plugged in the initial velocity at the time 0 s, right before she dropped the book)
If I have the time, I could find the distance. If V = -69.9 and a = -10 it took... 6.99 s. I have most of the variables for E3. I plug it in, and I find the top of the window is -244.3. The total distance is then 244.3."
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As you can see, I employ a method of "find the easily found unknown" hoping it will lead to the wanted unknown. I think that's a trait of my maths mindset.
So how do I get better at thinking about physics? TIA. Hopefully this isn't a weird question.

 

[Tsunoyukami]

Your approach is the same approach I was taught in high-school level physics. It was termed the GRASP method (Given; Required; Assess; Solve; Paraphrase). I think this is a very useful method while one is being introduced to problem solving, a skill which is developed by completing more and more physics problems.

In general, for high school level physics this approach will be "all you need". The vast majority of problems you will face are simple enough that this approach works surprisingly well. As you encounter more and more advanced problems you might find this approach becomes less useful - or maybe it will retain its utility.

To answer your question, however - you get better at (thinking about) physics by doing physics. You have to do physics and you have to make mistakes and learn from the mistakes you make and always ask "why" what you did was wrong. Sometimes you might just make a math error, forgetting a negative sign here or there, but sometimes you'll discover some kind of more subtle physical property of a system by making mistakes or overlooking something simple.