Test a water jet with a graph
You will be able to: Combine ideal efflux and projectile motion to design and interpret a linearized experiment.
How can a landing distance test the tank-outflow model?
A small hole sends a jet horizontally from a tank. Measure how far it travels before landing a fixed distance below the hole. Increasing the water level should increase that horizontal range, and a graph can test the predicted relationship.
A useful starting point: Water leaving a tank: speed from a height difference →
Words and symbols before equations
- h
- Water surface height above the outlet center, in m.
- H
- Vertical drop from outlet to landing level, in m; distinct from h.
- R
- Horizontal distance from outlet to the jet’s landing point, in m.
- Linearized graph
- A plot of transformed variables that the model predicts will be straight.
What this picture assumes
Synthetic ideal predictions for a horizontal water jet, g=10 m/s². Torricelli assumptions, no air drag, fixed outlet geometry. Graph compares R² with h at the selected fixed H. These are not experimental measurements.
Connect the picture to the physics
For a horizontal launch, vertical motion gives H=½gt², so flight time t=√(2H/g). Torricelli gives initial horizontal speed v=√(2gh). Horizontal range is R=vt=2√(hH), hence R²=4Hh. Here lowercase h sets exit speed and uppercase H sets flight time.
Hold H and outlet geometry fixed. Vary h, measure R during short intervals with nearly constant water level, and repeat. Plot R² vertically against h horizontally: predicted slope is 4H, with units of meters. Measure both heights from the outlet center and record uncertainty in the landing region and water level.
The prediction assumes a small horizontal outlet, negligible surface speed, no air drag, and ideal efflux without jet contraction or losses. Real jets can spread or slow; a slope different from 4H is evidence to investigate measurement bias and model limits. Calculated synthetic points do not validate a real apparatus.
A worked example, step by step
An outlet is H=0.50 m above the landing level, and the water surface is h=0.80 m above the outlet. Use g=10 m/s². Predict speed, flight time and range.
- v=√(2gh)=√16=4 m/s.
- t=√(2H/g)=√0.10≈0.316 s.
- R=vt≈1.265 m.
- R²=1.60 m², also equal to 4Hh=4(0.50)(0.80). A plot of R² vs h should have slope 2.0 m for this fixed H.
Do not interchange the two heights. The tank’s water head h controls launch speed; the external fall H controls time in the air.
Why is R² versus h straight while R versus h curves?
Compare with an explanation
Because R²=4Hh is linear in h, whereas R=2√(hH) has square-root dependence.
Predict. Change one thing. Explain.
Change h at fixed H and compare the calculated landing range with the R²-versus-h graph. Then change H and predict the new slope. All points are synthetic predictions, not measurements.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
h=0.8 m; external drop H=0.5 m. Exit v=4 m/s; flight time=0.3162 s; range R=1.265 m. R²=1.6 m²; graph slope 4H=2 m. Synthetic ideal prediction.
Synthetic ideal predictions for a horizontal water jet, g=10 m/s². Torricelli assumptions, no air drag, fixed outlet geometry. Graph compares R² with h at the selected fixed H. These are not experimental measurements.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant force, motion or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionPlan an outflow test with fixed H=0.40 m. (a) Name the variable to change and the quantity to measure. (b) State graph axes. (c) Predict the slope with units. (d) Give one model limitation or measurement improvement.
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Compare with the answer and four-point rubric
- 1 point: Change water head h; measure horizontal range R while maintaining nearly constant head during each short trial.
- 1 point: Vertical R² (m²), horizontal h (m).
- 1 point: Slope=4H=1.60 m.
- 1 point: Example: repeat trials and mark the spread of landing positions; or account for a nonhorizontal jet, changing water level, contraction, losses or height-reference error.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Which height sets ideal flight time?
H, the outlet-to-landing vertical drop.
RECALL 2Which graph should be linear?
R² versus water head h at fixed H.
RECALL 3Does agreement with a synthetic graph validate a real experiment?
No; real data and uncertainty analysis are needed.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Test a water jet with a graph
- Horizontal ideal jet: t=√(2H/g), R=2√(hH).
- R² vs h has slope 4H for fixed H.
Remember: Do not interchange the two heights. The tank’s water head h controls launch speed; the external fall H controls time in the air.
Conditions: Synthetic ideal predictions for a horizontal water jet, g=10 m/s². Torricelli assumptions, no air drag, fixed outlet geometry. Graph compares R² with h at the selected fixed H. These are not experimental measurements.
Refresh Kid · Unit 8 · Objectives 8.4.A, 8.4.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 8.4, objectives 8.4.A, 8.4.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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