Unintentional Physics Lesson- 2012-09-06

     Today a student walked into class and told me that they had a physics related debate all day that they wanted to settle.  Usually this means that I need to just answer a physics related question or misconception.  This time, however, was different because the debate came out of left-field, almost literally.
     The debate was about one student's claim regarding his own athleticism.  As they originally put the claim he said that he could throw a baseball 30 meters in under 1 second.  I wanted to clarify the distance because I didn't think that the baseline was measured in an even metric number, so after confirming that distance down a baseline was 90 feet which converts to 27.432 meters I said let's test it.  So we got a measuring tape, a trundle wheel, stopwatches, and a digital camera and headed to the gym to test it.  We chose the gym because of weather and because I wanted a more consistent background for the camera, as well as the confined space which has the ability to contain students who have trouble staying focused.
     So we measure 90 ft on the diagonal of the basketball court and then he started warming up.  I used the that time to explain to the timers what their job was and where to stand so that they'd be out of the way of the filming as I was up in the bleachers trying to catch the toss on my camera.
Here's the first take, without being slowed down:

The pitch leaves his hand between 6.28-6.31 and the camera does not track the ball well, but it appears that the catcher has the ball between 7.17-7.32.  This puts the pitch between 0.86 s and 1.04 s.  Taking the mean or median the claim is true, but the video is hard to follow and we had other data collected and no way to accurately review the film while testing.

   The frame rate of the video is 30 frames/second so the next data point was to try to slow the video down.

It is hard to count the individual frames, but it appears that the ball travels in 28 frames +/- 3 frames.  This gives a time of 0.83-1.03 s.  Again mean and median would support the claim.  However, my camera does have a better option that I switched to.

   The camera has a "Sports Mode" that takes a burst of up to 30 shots at a frame rate of about 13 frames/sec with the trade-off of low-quality images.  Those images are in the slideshow that follows [click on the icon in the bottom right corner and then click on the album title on the new image to go to a larger version of this slideshow].


Again, counting together in class we came up with 12 frames +/- 2 per pitch.  Again giving us values that are borderline low but with included uncertainty the claim could be true or false (0.77-1.08).

     Of course, we had the stopwatches with us also and recorded all of that data, although the recorder did not include who each time came from or which pitch was which.  That data is in the table that follows, and all seems to indicate that the pitch is faster than 1 second, but if we factor in the students' reaction times these values again fall within a narrow border around 1 second.

     This leads us to two options.  The first one is unsatisfactory, but to concede that the student can pitch faster because the data tends to indicate the low side of 1 second rather than the high side and would average out to be less than 1 second.  Or, we can attempt to find a better way to measure the speed of the ball, which allows us to extend the activity and debate a little longer and come to a more firm and decisive conclusion.

     A radar gun would be nice, but we don't have access to one.  Another option is to use motion sensors, but again we're limited by access as well as the ability of the devices to detect such a small object.  The final option is to film the release of the ball up close and instead attempt to determine the speed of the ball and from there calculate the travel time.  To this end we are setting up a contrasting background and a well lit area for filming this and will attempt to film it and then analyze the video.

   Considering we were going to go over a homework assignment and then the students were going to do seat work today this was a much more entertaining and informative lesson and the debate continues as will the discussion here.

Note: This reminded me of an article from the author of the online comic xkcd in his new section "What If" about throwing a baseball at nearly the speed of light.  Reading that article became homework for physics students after we did this impromptu lab.  You can read the article here.