- Determine the length of a particle’s path in space by using the arc-length function
- Calculate and understand what curvature means for curves in space
- Understand what normal and binormal vectors tell us about a curve’s behavior
Designing a Roller Coaster Track
You’re part of an engineering team designing a new roller coaster for an amusement park. The track follows specific mathematical curves to ensure rider safety and excitement. You need to calculate the length of track sections to determine material costs, analyze how sharply the track curves at critical points to ensure safe G-forces, and understand the geometry of the curve to properly position support structures. The track’s path is described by vector-valued functions, where distances are measured in feet.