The Waterfall Swing
Functions & Equations
The waterfall shuts off just before the rider swings through it — model both motions to find the safe timing window.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
A fairground or theme-park waterfall swing drops a rider through a curtain of water that switches off just before they arrive, so they pass through dry. Two separate motions have to line up: the rider swinging on a rope like a pendulum, and the water falling under gravity after the valve closes. Model each motion as a function of time, and you can work out exactly when the water needs to cut off for a given swing length and drop height — and how much timing error the ride can tolerate before someone gets wet.
Guiding Questions
- The swing rider drops through a waterfall that switches off just in time. What two motions must be synchronised?
- Model the rider as a pendulum and the water as free fall. Write both positions against time.
- For real dimensions, when must the water cut off so the rider passes through dry?
- What is the time margin of error? How does it change with a longer swing or higher waterfall?