Where should a pool ball hit the cushion? The geometry of bank shots

Why it makes a good exploration

Bank shots are pure geometry — angle in equals angle out — until spin and the cushion get involved. Testing the geometric prediction on a real table gives clean data and honest reflection.

The mathematics you'll need

• Reflection in a line and coordinate geometry
• Equations of lines and intersections
• Angles and trigonometry
• Mean error and spread

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

Film 30+ bank shots from above with a phone and measure contact points and angles with Tracker.

• Tracker video analysis — Free tool to track an object frame by frame in a video and export its x–y coordinates.
• GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.

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

1. Derive the mirror-image method.
2. Compute predicted contact points.
3. Measure real shots.
4. Compare and analyse errors.
5. Reflect on speed, spin and cushion geometry.

Showing personal engagement

• Use a table you play on.
• Test fast versus slow shots.
• Extend to two-cushion shots.

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

Taking it further

Model a correction for cushion compression and see if predictions improve.