Relative Velocity and Shaky Cams

I'm working on some of the first few days in AP C next year, and we're doing relative velocity then. I don't really have time to do it in Honors these days, and the AP kids certainly get on top of it very quickly, so I can really put it to bed in about a day with them if I wait, instead of needing a little more time the year before and then taking some time to do some review applications in the second year.

Anyway, here's my progression for that day (95 minutes):

• Frame the need with a video. I made this shaky-cam video of a ball rolling on a table (click through to see video). The motion's certainly odd, with direction changes that seem strange. I only show this one at full speed. Update: here's a link to the video.

• We use Logger Pro to track and model the motion, and the position graphs definitely look weird. Point out to them during the process that they can get a sense for how the speed is changing by looking at the sizes of the blurs. Speed and direction are changing, and (maybe) they won't be able to pick out the underlying motion at this point. 

• Now that we know that there's an issue to be solved and they have discussed the differences between looking at the motion from the camera's POV and the table's POV, I introduce an easier question to tackle, Dan Meyer's escalator/stair video, which they develop a method to solve pretty easily and successfully (though not super-quickly, with the data-taking and wringing of hands about distances and natural units):

Boat In The River — Question from Dan Meyer on Vimeo.

• If we are to apply this model to the first problem to determine what the motion really was, we can add calculated columns in Logger Pro to un-shake the motion and determine what type of motion it really was. Scaling the video (ball diameter is 3.3 cm) lets you calculate initial v and angle, acceleration, etc. as well, if you're into that sort of thing.

I want to seed the concept early and revisit it a few times during the term, so that going to the center-of-mass reference frame for collisions isn't as much of an abstract stretch as it could be.