Tuesday, July 15, 2014

It's a bird, it's a plane, it's a projectile!

Model Summary:  2D Motion of a Particle

Scenario - How can we tell whether a basketball will make the shot, given a motion map of its position at times early in the shot?

Force Diagram - Unbalanced downward Force_{Earth_on_Object} ("Feo - the ugly force"), with no horizontal forces

Motion Graphs

  • vertical position vs. time - downward facing parabola (assuming up is +)
  • horizontal position vs. time - linear with positive or negative slope depending on which direction object moves
  • vertical velocity vs. time - linear with negative slope (assuming up is +) equal to -10 m/s/s, similar to 1D free fall
  • horizontal velocity vs. time - constant
Motion Map - Position of dot shows change in both horizontal and vertical position, following parabolic path
  • dots have even horizontal spacing and constant-length horizontal velocity vectors due to constant velocity horizontal motion (no horizontal unbalanced forces)
  • dots have changing vertical spacing and direction and length of vertical velocity vectors due to constant acceleration horizontal motion (unbalanced vertical Feo)
Equations - 
  • Basically just the CVM equations for horizontal motion and the CAM equations for vertical motion... except...
  • The two are linked by time -- the object has the same amount of time in air, for both the horizontal and vertical components of its motion. 

Projectile Motion Implementation

I have not done projectile motion with my ninth graders, and I don't intend to.  I suppose the discussion of the independence of the components of the motion using video tracking might be a fun end-of-the-year / review activity if there were time.  It does tie together a lot of good things about the constant velocity model, constant acceleration model, balanced forces, unbalanced forces, and vectors.  On the other hand, without trig at least some of the typical projectile scenarios are, I think, out of their grasp.  Maybe they could handle horizontally launched problems?

I have done projectile motion with my eleventh graders, and I did it with a similar video tracking approach to the introduction.  Like many workshop participants, I did it after 1-D motion and before forces, and I'll rethink that placement next year.  My students relatively easily caught the independence and distinct behavior of the horizontal and vertical motion components, but had a harder time understanding the implicit clues about velocity and position in the wording of particular problems.   Those might be easier to understand if they already had forces under their belts?

As mentioned elsewhere, I found the practicum challenging, and I'll be looking for a way to do it that doesn't require the expensive projectile launchers and makes the math a little more approachable for more of my students.

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