IA idea · Sport

What is the best angle to shoot a free throw?

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

Research question

Which release angle requires the least launch speed for a free throw from my release height, and how much margin for error in speed does each angle allow?

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

Why it makes a good exploration

Players are taught to shoot with an arc — but how much arc? Projectile equations give the minimum-speed angle, and the “margin for error” question makes the answer practical rather than theoretical.

The mathematics you'll need

Projectile motion equations (explain the physics used)
Trigonometric identities and rearranging for v²
Differentiation to minimise launch speed
Sensitivity: how a speed error changes where the ball lands
Comparison with filmed shots

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

Measure your release height; film your own shots and estimate release angles with Tracker.

Tracker video analysis — Free tool to track an object frame by frame in a video and export its x–y coordinates.
Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

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

Set up the trajectory equations with release height and hoop distance.
Derive v² as a function of angle.
Find the minimum-speed angle.
Analyse tolerance to speed errors at different angles.
Compare with your own filmed shots and reflect on air resistance and the rim size.

Pitfalls that cost marks

Ignoring release height.
Treating the hoop as a point with no size.
Quoting results without checking against real shots.

Showing personal engagement

Film and analyse your own shots.
Compare a tall and a short player.
Explain why the optimum for accuracy is not the minimum-speed angle.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Include the hoop's diameter to find the range of successful angles for a given speed.

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).