Math IA Video Analysis With Tracker: Projectile Motion

Sport and motion topics make great maths explorations, because you can generate your own data and because it's easy to show real personal engagement. I've coached several, from a basketball release angle to topspin in tennis. The maths is rarely the problem. The data collection is. Here's how to get data that's actually usable. For a finished, annotated example, see what a full maths exploration looks like.

The tool: Tracker

Tracker is free, open-source video analysis software from the Open Source Physics project. You load a video, set a scale, click on an object frame by frame (or let it auto-track), and get position, time, velocity and angle data you can export to a spreadsheet. It runs on Windows, Mac and Linux.

Film it so the data is usable

Most bad video data comes from bad filming. The rules I give students:

Camera exactly side-on (90°) to the plane of motion. If the camera looks at the motion from an angle, every distance and angle in the video is distorted.
A scale reference in the plane of motion. Tape of a known length on a wall, a metre stick or a court line, at the same distance from the camera as the motion. Tracker uses it to convert pixels to metres.
Slow motion. Most phones film at 120 or 240 fps in slow-mo, which gives far more data points per throw or shot.
Tripod at a fixed height and position, the same for every trial. A cheap Bluetooth shutter means you don't move the phone between takes.
Your own footage, not someone else's. Professional players on YouTube look tempting, but you don't know the camera angle, distance or frame rate, so the data can't be trusted.

Design for analysis, not just for data

One relationship. Pick one input you can vary (release angle, racket-face angle, launch speed) and one output (distance, height, accuracy). Hold everything else as constant as you can.

Lots of trials. For a sports exploration, plan around 50–100 trials if your topic allows it. Individual human movements vary a lot, and you need enough data to see the pattern through the noise.

Build in variation on purpose. If you want to find an optimum angle, you need trials on both sides of it: some flat, some steep. A student who only films their "good" shots can't locate a maximum.

Measure something continuous. "In or out" throws information away. A ball that lands 2 cm out and one that lands 2 m out count the same. Measure the distance from a target point instead, and keep in/out as a secondary result. Continuous data gives you regression, optimisation and error analysis to work with.

A helper with a tick sheet. Trial number, the input setting, and anything unusual (wind, a mishit). It saves hours of matching videos to results later.

The maths you can do with it

Fitting a model to a trajectory: a projectile path is close to a parabola, so fit a quadratic to the position data. Compare it with the theoretical model, and discuss the difference (air resistance, spin).
Optimisation: model accuracy or distance as a function of angle, then find the maximum or minimum with calculus or technology.
Regression and correlation (especially for AI): the strength of a relationship across trials, the residuals, and which model fits best.
Error and uncertainty: frame-rate limits, scale-reference uncertainty, clicking precision in Tracker.

Choose the maths that answers your question, at your course level, and explain why you chose it. Using maths you understand well beats name-dropping something advanced you can't explain.

How it's marked

Explorations in AA and AI share the same criteria (20 marks): Presentation 4, Mathematical communication 4, Personal engagement 3, Reflection 3, Use of mathematics 6. These apply to the current courses, examined until November 2028; the revised courses first examined in May 2029 use new criteria. The maths IA criteria guide goes through what each one rewards. A self-designed motion study is strong on personal engagement, because you made genuine decisions. Make those decisions visible in your write-up: why this angle range, why this many trials, what you changed after a pilot run.

Reflection marks come from thinking critically about your own process and results: limitations of the model, of the filming, of the sample, and what the results actually mean. Not a paragraph at the end saying it was fun.

Run a pilot first

Before the real data day, do a ten-trial pilot. Load it into Tracker and check the scale works, the tracking is clean and the frame rate is enough. You'll find at least one problem. Better to find it with ten trials than a hundred.