Brachistochrone and Tautochrone curves
applied
A year-round outdoor freestyle centre for skiers has opened in the Swiss resort of Leysin. (Dry Slope News)
Introduction
‘Le Bag’ features two dry ski ramps leading to two jumps, one 16 metres high aimed at less experienced jumpers, the other 22 metres high for the most experienced. The jumps, covered in JF Dryski matting, take freestyle skiers and boarders into the air above a sloping 55m X 25m big air bag. The 26-metre-high top of the run into the jumps is accessed via conveyor lift from the base.
Guiding Questions
- What mathematical models apply to this situation?
- What data do you need to collect and how will you analyze it?
- What assumptions are you making in your mathematical model?
- How can you validate your mathematical conclusions?
- What are the limitations of your approach?
Key Mathematical Concepts
Optimization
Physics
Calculus of Variations
Cycloids