Academic purpose and safe learning
Students build a two-dimensional kinematics model under constant downward gravity. They decompose vectors, solve vertical impact time, find horizontal range and explain independence only under stated no-drag assumptions. These lessons support the quantitative modeling and scientific inquiry practices of the broader HS-PS2-1 physics unit; they do not individually claim to fulfill all Newton's-law performance expectations.
Prerequisites: Week 02 coordinates and displacement, Week 03 velocity/acceleration, slope, graph axes and algebra; Week 04 also uses introductory sine/cosine; Week 05 uses squaring and means. Differentiation: provide a partially labeled diagram and pre-calculated table for foundation learners; use the full simulator for core; ask extended learners to critique simplifying assumptions.
Monday · The Two-Object Drop Mystery
Target: Explain horizontal/vertical independence under constant gravity and negligible drag.
Suggested pacing: 8 minutes phenomenon and prediction; 17 minutes explicit reading and worked example; 15 minutes data/interactive investigation; 10 minutes written reasoning; 5 minutes correction and exit prompt.
Suggested check: If horizontal speed doubles but vertical initial conditions remain identical, should impact time change in the no-drag model?
Tuesday · Vectors, Angles and Components
Target: Resolve an initial velocity vector into horizontal and vertical components with units.
Suggested pacing: 8 minutes phenomenon and prediction; 17 minutes explicit reading and worked example; 15 minutes data/interactive investigation; 10 minutes written reasoning; 5 minutes correction and exit prompt.
Suggested check: Why do vx and vy change when you change only the launch angle?
Wednesday · Trajectories and Impact Time
Target: Find flight time and range analytically and verify the result against a graph/table.
Suggested pacing: 8 minutes phenomenon and prediction; 17 minutes explicit reading and worked example; 15 minutes data/interactive investigation; 10 minutes written reasoning; 5 minutes correction and exit prompt.
Suggested check: When does a 45° launch cease to be the maximum-range choice?
Thursday · Virtual Projectile Laboratory
Target: Run controlled, safe projectile simulations, record multiple trials, and calculate impact time and range.
Suggested pacing: 8 minutes phenomenon and prediction; 17 minutes explicit reading and worked example; 15 minutes data/interactive investigation; 10 minutes written reasoning; 5 minutes correction and exit prompt.
Suggested check: What would changing both speed and angle at once prevent you from identifying?
Friday · Projectiles: Explain and Defend
Target: Construct a quantitative CER on independent motion components and correct model misconceptions.
Suggested pacing: 8 minutes phenomenon and prediction; 17 minutes explicit reading and worked example; 15 minutes data/interactive investigation; 10 minutes written reasoning; 5 minutes correction and exit prompt.
Suggested check: Why is an air-drag experiment not directly comparable to this ideal calculation?
Worked reference answers
For h=19.6 m, vy0=0 and g=9.8 m/s², t=√(2h/g)=2.0 s. With vx0=5 m/s range=10 m; with vx0=10 m/s range=20 m. Launch v0=10 m/s at θ=30° gives vx0≈8.66 m/s, vy0=5 m/s. Level-ground flight time 2vy0/g≈1.0204 s, range≈8.84 m and apex height≈1.28 m. For complementary 30°/60° launches at equal initial speed and level-ground conditions, ideal ranges agree within rounding; time and apex differ. This is not true of all launch heights or real-world drag.
20-point CER review rubric
- Claim · 4
- Scientific answer limited by defined system and assumptions.
- Numerical evidence · 4
- At least two valid calculations or observations with units and data provenance.
- Interpretation · 4
- Accurate vector components, time, range or axis interpretation.
- Reasoning · 4
- Correct physical equation and logically connected explanation.
- Limitations · 4
- Fair counterclaim, potential uncertainties and a useful next experiment.
Teacher review target: 16/20 (80%). Allow revisions and preserve evidence of initial work separately.
Common misconceptions and extension
- Horizontal velocity changes vertical impact time even without drag. — have students locate the invalid assumption and supply a correction.
- Every launch has a 45° maximum range regardless of height. — have students locate the invalid assumption and supply a correction.
- The apex is always at the impact time. — have students locate the invalid assumption and supply a correction.
- A trajectory plotted against x represents a time graph. — have students locate the invalid assumption and supply a correction.
- Simulation predictions certify safe real launches. — have students locate the invalid assumption and supply a correction.
Public open-book practice items and browser-local evidence are not secure, supervised final examinations. Teacher-verified assessments require a separate educator-controlled process.
Offline resources and portfolio
Preserve existing `khae_high_science_evidence_v1:` browser-storage keys and dormant STOS assets. New standalone lesson notes use separate namespaced keys and JSON export/import. No cross-device cloud synchronization is claimed.