Dan Meyer made this awesome photo. He posted it so that others could look at it and come up with lesson ideas to use with this. There are some very good suggestions in his comments. I wasn’t going to analyze this because I didn’t want to rob some students of the opportunity, but I can’t resist. Also, I doubt the first step a student would use would be to google for the answer. HA! I just caught you, you googling student.
Ok – I will try not to post any data. However, I will post some info on how I analyzed this.
The photo is a composite image from a video clip of a person throwing a tennis ball. It shows several instances of the tennis ball in the video. Clearly, the first step is to get position-time data for the ball. Well, I don’t really know how much time is in between each instance of the ball, but I can get x-y data. I will use Tracker Video – my favorite free java-based video analysis program. I admit that I don’t use all the features of this program – but people get stuck in their ways.
After launching the program (and saving Dan’s image), go to “video -> import” under the file menu and find the image. Tracker will import it even though it is just an image (tracker also has spectral analysis tools). The first thing I do with a video (or image) is to set the scale if I can. Dan was thoughtful enough to use a football field. I can use that known distance. Here is the scale button.
This is what the scale arrow looks like. It also has a number on top of that. Double click it to set the distance you want (I am not showing the whole arrow).
Next, I am going to do something that I am not sure is a feature or a trick. I am going to tell Tracker to use 20 frames of this video. Yes, I know it is just a picture, but this will work. You can even set the time interval also if you want – but I really don’t know what this time interval is. To set this stuff up, click the movie settings button – looks like this:
This will bring up a menu where you can choose the video settings (like how long and step size). You should always at the very least use this to cut off unneeded stuff from a normal video.
Now to get to the data. To mark the location of each ball, you first need to add a “point mass”. Here is the menu.
After that, simply shift click on each of the images in the image (which is now a video). When you click on an image, Tracker will move to the next frame (which looks exactly the same). Tracker will now show you the data and you can do all sorts of cool stuff that I don’t really use (but it’s good stuff). I just copy the data and paste it into a spreadsheet or something. Actually, I like LoggerPro.
From there, you can fit a function to the data. Here are the questions I came up with (that I will not answer in case someone wants to use this):
- What should be the acceleration in the x-direction?
- What should be the acceleration in the y-direction?
- Using the above question, can you find the time between images?
- How fast was the ball thrown?
- How high above the ground did the ball go?
- Will the ball land in the trash can?
- Is there an error in the image? (not sure if that was intentional or not)
More advanced question: was air resistance significant? How do you know?
As mentioned in Dan’s comments on his site, you could use some much simpler methods for getting this data – even printing it out and using a ruler would work.