Wednesday, February 2, 2011

Quadratics Revisited: The Falling Object Model

I keep hoping that I can use this to help kids derive the falling object model. I'm getting close. I exported the video at 6fps so 1/6 second elapses between strobes. I'd like some feedback on this before I roll it out to my students. How intuitive is it to use both applets together?



This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com


Once you have plotted your points, use the FitPoly function. Simply enter "fitpoly[A,B,C,D,E,F,G,H,I,2]" to plot a quadratic function.



This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com


If this proves to be useful, I'll dial it all in and post the still, video and applets for download.

10 comments:

Dan Anderson said...

Pretty nifty.
It is intuitive to me on how to use the applets together, will it be to 7th/8th graders? Probably?
I like it though. Are you going to show the video first? Or let them have at the applets?

Frank Noschese said...

I can't figure out how to use the applet. Help?

David Cox said...

@Dan
My kids will most likely have a go at it. I think I'm going to show the video, add timecode and cut it off before the ball hits the ground.

@Frank
Place the white circle around each strobe and record the distance from the ground. Elapsed time between strobes is 1/6 second. Enter the ordered pairs into the second applet and use the fitpoly function to do the quadratic regression.

Frank Noschese said...

So students are moving the white circle to the pictures of the ball (which you made), getting the height(which the computer gives them), and graphing them with a program to find the parabola (which the computer calculates). Seems like the kids aren't doing much thinking, just pointing and clicking.

These are middle school kids, right? Do they know how the computer calculates the height? Do they know how the computer fits the parabola?

Here's what I might do. Give each kid an overhead transparency and marker to put onto the computer screen to mark the position of the ball every frame (or every 2, 5, n frames or whatever). Given the initial height of the ball, have them use proportions to determine the heights of the ball on their transparency.

Then go to Data Flyer http://www.shodor.org/interactivate/activities/DataFlyer/ to input the points and use the manual curve fit sliders to fit the function to their data. They will have a better feel for how each coefficient manipulates the curve.

Repeat video analysis for ball tossed straight up. Repeat for ball tossed between two people. What's the same/different about the equations for all three vertical motions?

David Cox said...
This comment has been removed by the author.
David Cox said...

...and that's why I put this out here before putting it in front of my kids. Thanks, Frank.

David said...

I think I can do the same thing in GeoGebra. I can define variables a,b and c with sliders and let the kids mess with the regression themselves. The main reason I made the applet was to see how close I could get to the falling object model by analyzing a still picture.

I definitely want my kids to do most of the lifting. I'm just still trying to figure out how to best do that.

Frank Noschese said...

Instead of the video+overhead, you could also give the kids a handout of the time lapse photo you made, have them measure directly on the handout and the use the applet with sliders to fit the curve.

Krishna said...

I know this is an older post, but I just ran across it. I'd love to make my own version of your "strobed" picture. Is it easy to explain what you did? I'll follow along with your explanation as best I can. Thanks!

David Cox said...

Dan did a pretty good job of explaining the process here.