Show that launching from a height destroys the 45-degree rule
Three steps, the way the exam actually works: work through the lab, write down your own measurements, then answer a 9-point free response. What you recorded goes to the grader with your writing, so a conclusion that does not follow from your own numbers will cost you the point — exactly as it would with a real reader.
Predict before you look
- On level ground the range formula is R = v₀² sin(2θ)/g. From that expression alone, which angle maximizes range, and which pairs of angles give equal ranges?
- The range formula is derived by setting the vertical displacement to zero. Write down, in one line, why that derivation stops applying if the projectile lands below its launch point.
Nothing to submit here — these are to think through, so the prediction below is an informed one rather than a guess.
Commit to an answer now. It is not graded and being wrong costs nothing — the point is to have something specific to reconcile against once you have the data.
Answer every prediction to unlock the lab. A sentence is enough.
Run the investigation
Predictions first
The procedure and the simulation unlock once you have committed above. Observing before predicting is how a wrong intuition survives a lab intact.
Record what you measured
These are your numbers, not ours. The grader sees them, so your conclusions have to follow from what you actually recorded.
| Range at 30°, launched from the ground | m |
|---|---|
| Range at 45°, launched from the ground | m |
| Range at 60°, launched from the ground | m |
| Range at 30°, launched from 20 m | m |
| Range at 45°, launched from 20 m | m |
| Range at 60°, launched from 20 m | m |
| Angle giving the greatest range from 20 m | ° |
| Flight time at 30° from 20 m | s |
| Flight time at 30° from the ground | s |
Answer the free response
Using your two sets of readings: (a) State whether 30° and 60° gave equal ranges from the ground, and whether they did from 20 m, citing all four numbers. (b) Explain, using the derivation of R = v₀² sin(2θ)/g, exactly which assumption fails when the launch point is above the landing surface. (c) State the range-maximizing angle you found from 20 m and explain physically why it is below 45°. (d) Using your two flight times at 30°, explain what the extra launch height does to the time available and why that favors a flatter launch.
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