The Centre for Near Earth Objects monitors potential impact risks of comets and asteroids with the Earth and explore opportunities to collect information from these galactic time capsules. Students use calculus to determine the minimum distance between two curves. The curves represent a simplification of the Earth’s path and the comet or asteroid trajectory.
- Use Pythagoras to form equations.
- Use calculus to determine local max / min
- Use a simpler problem to solve a more complex problem
About the Lesson
Students determine the minimum distance between two curves by building understanding through simpler problems. Part one involves using Pythagoras and calculus to determine the minimum distance between the origin and a parabola. Part two considers the second curve as a series of points therefore drawing upon the logic, reasoning and methods used in part one. Students determine local minimums, draw upon the geometric relationship where these minimums occur to find the minimum distance between the two curves.