Single-problem validation

Projectile launched from a cliff

1 student taskFull packWorkbench

Projectile launched from a cliff

Run one observed attempt for this mechanics model before changing problem scope.

Full validation pack
  1. Run one student on one problem at a time; do not demo the full site first.
  2. Start from the public problem page, then switch to Solve mode before any answer-key exposure.
  3. Record attempt time, finish state, first hesitation checkpoint, first wrong path, and whether the reveal changes their explanation.
  4. Paste the copied Solve-mode attempt snapshot into notes as evidence, but do not treat it as a score or success verdict.
  5. Count the visible corrections or checker recoveries before the student can explain the governing equation in their own words.
  6. Record the exact first-success quote or mark no usable evidence; do not infer clarity from a correct final answer.
  7. Show the tutor the worksheet answer key only after the student attempt, then capture concrete reuse or rejection reasons.

Decision gate

Student task

Solve modeProblemWorksheet

Student can explain why "t = 3.3 s" follows from the diagram state and givens.

Focus checkpoints

  • Choose projectile axes and origin
  • Resolve the launch velocity
  • Write the vertical position equation
  • Solve the quadratic for flight time

Observe for

  • Does the student avoid this trap without prompting: Using the full launch speed as the horizontal velocity instead of v_0 cos(theta).
  • Which checkpoint caused the first real hesitation or correction?
  • Did the reveal help them explain the equation, or only copy the next algebra line?

Equation-choice spot checks

  • Choose projectile axes and originWhat feature of the diagram, sign convention, or givens makes "Choose projectile axes and origin" the right next equation?
    Listen for: Use independent horizontal and vertical axes. The launch point starts above the ground, so the vertical position equation must carry y_0.Flag if: Making gravity positive in the +y upward convention.
  • Resolve the launch velocityWhat feature of the diagram, sign convention, or givens makes "Resolve the launch velocity" the right next equation?
    Listen for: The horizontal component stays constant, while the vertical component changes under gravity.Flag if: Using the full launch speed as the horizontal velocity instead of v_0 cos(theta).
  • Write the vertical position equationWhat feature of the diagram, sign convention, or givens makes "Write the vertical position equation" the right next equation?
    Listen for: At impact the ball is at ground level, y = 0. Gravity is negative because +y is upward.Flag if: Using the same-height range formula v_0^2 sin(2theta) / g even though the projectile lands below launch height.; Solving only for time to the top of the path, v_0 sin(theta) / g, instead of time to the ground.
  • Solve the quadratic for flight timeWhat feature of the diagram, sign convention, or givens makes "Solve the quadratic for flight time" the right next equation?
    Listen for: The positive root gives the time when the projectile reaches the ground. The negative root is an extrapolated time before launch.Flag if: Student can only quote "t = 3.3 s" without connecting it to the diagram state or givens.
  1. Open the Solve-mode link for Projectile launched from a cliff and ask the student to restate the target unknown before writing equations.
  2. Ask for the diagram state first: axes, direction assumptions, and the force or motion components they expect to use.
  3. Let the student attempt one scratch line before any checkpoint reveal, then use Check this line only after the attempt.
  4. If they stall, reveal one checkpoint and ask them to say which diagram element or given made that equation necessary.
  5. After the result checkpoint, ask for one sentence explaining why the chosen governing equation was the right model.

Tutor review prompts

  • Would you send /problems/projectile-from-cliff-range to a student stuck on this exact problem?
  • Which checkpoint would save you the most explanation time?
  • Which diagram label, assumption, or rubric row feels misleading or too thin?
  • What one change would make this problem page worth reusing in a lesson?

Tutor rubric cues

  • Setup (0 / 1 / 2)Axes, sign convention, model constraints, and linked-motion/origin choices are stated.Score descriptions
    • 0No usable evidence for this row, or the work contradicts "Choose projectile axes and origin".
    • 1Partly correct, but review this row's checkpoint signal: Making gravity positive in the +y upward convention.
    • 2Complete row: Axes, sign convention, model constraints, and linked-motion/origin choices are stated.
    Watch: Making gravity positive in the +y upward convention.
  • Components (0 / 1 / 2)Resolved components, force directions, normal/friction setup, or velocity split are correct.Score descriptions
    • 0No usable evidence for this row, or the work contradicts "Resolve the launch velocity".
    • 1Partly correct, but review this row's checkpoint signal: Using the full launch speed as the horizontal velocity instead of v_0 cos(theta).
    • 2Complete row: Resolved components, force directions, normal/friction setup, or velocity split are correct.
    Watch: Using the full launch speed as the horizontal velocity instead of v_0 cos(theta).
  • Net-force / governing equation (0 / 1 / 2)The main Newton's law or motion equation uses the right model, signs, and shared variables.Score descriptions
    • 0No usable evidence for this row, or the work contradicts "Write the vertical position equation".
    • 1Partly correct, but review this row's checkpoint signal: Using the same-height range formula v_0^2 sin(2theta) / g even though the projectile lands below launch height.
    • 2Complete row: The main Newton's law or motion equation uses the right model, signs, and shared variables.
    Watch: Using the same-height range formula v_0^2 sin(2theta) / g even though the projectile lands below launch height.; Solving only for time to the top of the path, v_0 sin(theta) / g, instead of time to the ground.
  • Result (0 / 1 / 2)The final rearrangement, numeric value, units, and direction/speed interpretation are correct.Score descriptions
    • 0No usable evidence for this row, or the work contradicts "Solve the quadratic for flight time".
    • 1Partly correct, but review this row's checkpoint signal: Reporting the vertical impact speed alone instead of combining v_x and v_y.
    • 2Complete row: The final rearrangement, numeric value, units, and direction/speed interpretation are correct.
    Watch: Reporting the vertical impact speed alone instead of combining v_x and v_y.

Projectile launched from a cliff session notes

Capture observed outcomes from real attempts: time, hesitation checkpoint, wrong path, copied Solve-mode snapshot evidence, recovery, equation-choice explanation, first-success evidence, manual tutor row scores, and tutor send-link decision.

Next-fix queue

Use after real attempts: carry only observed time, hesitation, wrong-path, recovery, equation-choice, first-success, manual tutor row-score, or tutor-rejection evidence into the next product slice. The evidence gate flags partial notes before they masquerade as product signals.

No observed attempts yet
Observed sessions: 0Ready for next-fix review: 0Need more observed evidence: 0

Run one single-problem Solve-mode attempt before choosing a product fix or adding another mechanics model.

No observed next fixes yet.

Projectile launched from a cliff

Solve modeProblemWorksheetBrief

Focus checkpoints: Choose projectile axes and origin; Resolve the launch velocity; Write the vertical position equation; Solve the quadratic for flight time

Tutor row-score template: Setup ___ / 2; Components ___ / 2; Net-force / governing equation ___ / 2; Result ___ / 2; reteach cue: ___

Seed from Solve snapshotPaste a copied Solve-mode attempt snapshot. Only filled starter fields are imported; placeholder blanks stay missing evidence.
Evidence checklistNeed all five evidence groups before this note can drive next-fix review.
  • Missingattempt time / finish stateAttempt time and finish state
  • Missingequation-choice evidenceEquation-choice explanation
  • Missingfirst-success quote or verdictFirst success-test evidence
  • Missingscratch, checker, or reveal evidenceWrong path or scratch line / Solve attempt snapshot evidence / Corrections before recovery / Reveal outcome
  • Missingmanual tutor row, tutor decision, or next-fix cueTutor row scores and reteach cue / Tutor send-link decision / Next fix before adding problems
Manual row-score summaryEnter observed 0/1/2 row scores to summarize manual tutor evidence.Blank row-score starters stay out of totals and do not count as grading.
Manual row-score helper0/1/2 rows from the existing tutor rubric. Blank starters do not count as evidence.
  • Setup ___ / 2Axes, sign convention, model constraints, and linked-motion/origin choices are stated.0: No usable evidence for this row, or the work contradicts "Choose projectile axes and origin". | 1: Partly correct, but review this row's checkpoint signal: Making gravity positive in the +y upward convention. | 2: Complete row: Axes, sign convention, model constraints, and linked-motion/origin choices are stated.Watch: Making gravity positive in the +y upward convention.
  • Components ___ / 2Resolved components, force directions, normal/friction setup, or velocity split are correct.0: No usable evidence for this row, or the work contradicts "Resolve the launch velocity". | 1: Partly correct, but review this row's checkpoint signal: Using the full launch speed as the horizontal velocity instead of v_0 cos(theta). | 2: Complete row: Resolved components, force directions, normal/friction setup, or velocity split are correct.Watch: Using the full launch speed as the horizontal velocity instead of v_0 cos(theta).
  • Net-force / governing equation ___ / 2The main Newton's law or motion equation uses the right model, signs, and shared variables.0: No usable evidence for this row, or the work contradicts "Write the vertical position equation". | 1: Partly correct, but review this row's checkpoint signal: Using the same-height range formula v_0^2 sin(2theta) / g even though the projectile lands below launch height. | 2: Complete row: The main Newton's law or motion equation uses the right model, signs, and shared variables.Watch: Using the same-height range formula v_0^2 sin(2theta) / g even though the projectile lands below launch height.; Solving only for time to the top of the path, v_0 sin(theta) / g, instead of time to the ground.
  • Result ___ / 2The final rearrangement, numeric value, units, and direction/speed interpretation are correct.0: No usable evidence for this row, or the work contradicts "Solve the quadratic for flight time". | 1: Partly correct, but review this row's checkpoint signal: Reporting the vertical impact speed alone instead of combining v_x and v_y. | 2: Complete row: The final rearrangement, numeric value, units, and direction/speed interpretation are correct.Watch: Reporting the vertical impact speed alone instead of combining v_x and v_y.