IA idea · Sport
Why don't long jumpers take off at 45°?
Research question
If take-off speed decreases as take-off angle increases, what angle maximises jump distance, and does it agree with the angles of around 20° measured in elite jumpers?
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Why it makes a good exploration
Projectile theory says 45°, but real long jumpers take off far lower. Adding the fact that athletes cannot jump upward as fast as they run forward changes the optimisation completely — a perfect lesson in modelling assumptions.
The mathematics you'll need
- Range of a projectile with a take-off height
- Modelling speed as a function of angle
- Differentiation to find the optimal angle
- Comparing with published or measured angles
Where the data comes from
Use published biomechanics data for elite jumps, or film your own jumps and track them with Tracker.
- Tracker video analysis — Free tool to track an object frame by frame in a video and export its x–y coordinates.
- World Athletics records and results — All-time lists, records and progression for every athletics event.
Real data for this idea
- Primary source: World Athletics records and toplists: All-time toplists. Opens on the men's 100 m: choose your event, copy the marks you need into your own table and cite the page and date. Licence: No reuse licence found: link and cite only.
- Also useful: Olympedia results. Use the event result pages; copy only the rows you need and cite each page. Licence: No reuse licence found: link and cite only.
There is no open reuse licence for these figures: copy only the values you analyse into your own table, and cite the page and the date. Links checked October 2026; we link to the data and never copy it. More free data sets.
A possible outline
- Derive range for constant speed (45° optimum).
- Introduce a speed–angle relationship and justify it.
- Optimise the new model.
- Compare with measured angles.
- Reflect on which assumption changed the answer most.
Pitfalls that cost marks
- Ignoring take-off height and landing position.
- Choosing the speed–angle relationship without evidence.
- No comparison with real jumps.
Showing personal engagement
- Film your own jumps at different angles.
- Talk to an athletics coach.
- Compare long jump and high jump.
See Criterion C: personal engagement for what examiners look for.
Which course is it for?
| Course | Fit | Maths to lean on |
|---|---|---|
| AA SL | Good fit | Range of a projectile with a take-off height; Modelling speed as a function of angle |
| AA HL | Good fit | Range of a projectile with a take-off height; Modelling speed as a function of angle |
| AI SL | Good fit | Range of a projectile with a take-off height; Modelling speed as a function of angle |
| AI HL | Good fit | Range of a projectile with a take-off height; Modelling speed as a function of angle |
Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.
How this idea reaches the top bands
Reflection (D)
For this idea, start with the weak points: ignoring take-off height and landing position; and choosing the speed–angle relationship without evidence. Say how each one affects your answer.
Use of mathematics (E)
SL: range of a projectile with a take-off height; modelling speed as a function of angle; differentiation to find the optimal angle; comparing with published or measured angles, each explained in your own words and carried out correctly.
How sport explorations reach the top bands in general: Sport IA ideas. Guides: A · B · C · D · E · self-grade sheet.
Taking it further
Fit the speed–angle relationship from your own jumps and re-optimise.
Extending it for HL
Add an HL technique the question genuinely needs: what an HL sport exploration adds.
See a complete IA, marked
How long does a skydiver take to reach terminal velocity? (AA HL) is a complete sport exploration, marked on every criterion.
Frequently asked questions
Which IB Maths course is this IA idea for?
It works for AA SL, AA HL, AI SL and AI HL. We rate it Solid: it needs some independent work beyond class examples.
What mathematics does this IA use?
Range of a projectile with a take-off height, modelling speed as a function of angle, differentiation to find the optimal angle and comparing with published or measured angles.
Where can I get data for this IA?
Use published biomechanics data for elite jumps, or film your own jumps and track them with Tracker. Checked sources and tools: World Athletics records and toplists, Olympedia, Tracker video analysis and World Athletics records and results.
Turn this idea into your IA
The planner opens with “Why don't long jumpers take off at 45°?” filled in: the question, the maths and the data sources.
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