Momentum components conserve separately
The mistake
Conserving the speed-like magnitude of momentum instead of x and y components.
Why it feels right
Momentum is introduced as p = mv, so it can look like one scalar amount.
How to catch it
A two-dimensional collision is solved with one momentum equation using magnitudes.
The first principle
Momentum is a vector. If external impulse is negligible, conserve p_x and p_y independently.
worked mini-example
A puck moving east breaks into two pieces, one moving north. What must the other piece do?
Common wrong move
Move south with the same speed.
Correct
Its momentum must supply both the original east component and a south component to cancel the north piece.
Test the repair MOM-07 · transfer
Make a fresh prediction before referring to the worked example.