IA idea · Sport

Why don't long jumpers take off at 45°?

AA SLAA HLAI SLAI HL Solid Also in: Calculus, Modelling

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?

Adapt it: change the place, the data or the comparison until the question is yours.

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

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

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.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

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.

Taking it further

Fit the speed–angle relationship from your own jumps and re-optimise.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).