1. Another Look at Length of Path Philip Rash NC School of Science & Math rash@ncssm.edu NCCTM Fall Conference Greensboro, NC October 30 2014

2. Outline Review of projectile motion (ignoring air resistance) Length of path (non-parametric & parametric) Modeling a falling object with air resistance Length of path using Euler’s Method, with and without air resistance (If time) Some sample student Calculus concepts: Differential Equations, Euler’s Method, Parametric Equations, Arc Length

3. Projectile Motion

6. (geogebra demo)

7. Projectile Motion – Maximizing Horizontal Displacement

8. Length of Path

12. (student activity handout)

13. Fall of a Skydiver - Intro

15. (skydiver excel sheet)

16. Length of Path, Reprise

17. Length of Path, Reprise Part 1

19. What about the launch angle that maximizes total distance traveled? Ignoring air resistance, we know the angle that maximizes horizontal displacement is 45 degrees. But 45 degrees doesn’t maximize the total distance traveled, but rather approximately 57.7 degrees.

20. (excel sheet – no air resistance tab)

21. Length of Path, Reprise

22. Length of Path, Reprise Part 2

23. Length of Path, Reprise Part 1

26. Length of Path, Reprise Part 2 Now what about the launch angle that maximizes horizontal displacement? total distance traveled? Depends on how much air resistance.

27. (excel sheet –air resistance tab) (student samples?)

28. A few “plugs” A summer program for rising 7 th – 12 th graders that fuses hands-on learning with online collaboration in unique STEM topics

29. Thanks! http://courses.ncssm.edu/math/talks/conferences/ Contact info: Philip Rash NC School of Science & Math rash@ncssm.edu

30. A summer program for rising 7 th – 12 th graders that fuses hands-on learning with online collaboration in unique STEM topics These high level courses are three weeks long; two weeks online & 1 week on our campus Tuition & courses announced Nov 1, 2014 Applications accepted Dec 1, 2014 Rolling admissions