Explicit physics instruction
A vector can be represented by perpendicular components. In two dimensions, horizontal and vertical components can be analyzed independently and recombined.
For right-angle components, resultant magnitude follows the Pythagorean theorem. Direction can be represented by an angle relative to a chosen axis.
Signs matter. A component west or downward may be negative depending on the coordinate convention; changing the convention changes signs but not the physical vector.
Vocabulary: component; resultant; coordinate system; magnitude; direction.
Worked example with reasoning
A displacement 3 m east and 4 m north has magnitude √(3²+4²)=5 m. Its direction is northeast; a more advanced description can use an angle from east.
Guided question
A walker travels 6 m east and 8 m north. Find the resultant magnitude and explain why 14 m is distance traveled but not displacement magnitude.
Independent work
- Resolve three supplied vectors into components.
- Recombine two perpendicular components.
- Draw one vector addition head-to-tail and one component diagram.
Misconception check
Vector magnitudes do not usually add arithmetically unless the vectors lie on the same line and direction.
Formative understanding check
Why is 6 m east plus 8 m north not a 14 m displacement?
Reveal response
Because the directions are perpendicular; the resultant magnitude is 10 m.
Mentor evidence conference
Ask Archaemenes to audit units, assumptions, coordinate choices, and evidence limits.
Teacher guidance
Foundation: Use grid-paper component diagrams.
Core: Solve component/resultant problems and state coordinate conventions.
Extended: Compare graphical and algebraic vector addition and quantify disagreement.