Solving problems

A repeatable procedure.

The routine

Sketch the situation. Draw the free body diagram. Choose axes. Write the equations. Solve symbolically, then substitute numbers. Check units and whether the answer is plausible.

Keeping symbols to the end makes errors visible and the result reusable.
If the number is absurd, the setup is wrong, not the arithmetic.

Choosing a method

Use forces when you need the detail of the motion, energy when you only need start and end states, and momentum when two bodies interact briefly. Picking well turns a page of algebra into two lines.