Here is video analysis data for a falling softball. Least squares on the
velocity data gave -9.83 +- 0.3 m/s/s. While the video was captured at 30
FPS, only every other frame was analyzed, and a different finite derivative
is used than in your message. For example, the velocity at t = 0.2 seconds
is calculated:
v = (0.504 - 0.909)/(0.267 - 0.133) = -3.022 m/s
The difference between this value and the one in the table are because of
truncation in the table.
Things you might try to improve your measurement error are:
* Use about seven or eight points across the entire vertical component of
your screen. You can adjust this using your camera zoom and your analysis
software.
* When using a ball in free fall, I've found it is more accurate to mark the
top, rather than the center, especially if you have to estimate the center.
Concerning your video camera question, I have used Hi-8, S-VHS, and VHS. All
have given reasonable results. The one most important item is a high speed
shutter.
Finally, concerning your comment about the price of a camera, capture board,
etc. exceeding a free fall apparatus, I agree with you. If you are only
going to use video analysis with freely falling objects, then the price is
prohibitive. However, if you use it for other lab experiments you will not
see the need for much of the apparatus you are now using for timing. Also,
as you use it, you will find that video analysis opens up experimental
possibilities that were not easily done using other techniques.
As a final thought, are you sure you are not dropping frames? The reason I
ask is your comment that your velocity data for free fall did not look
linear. Maybe you can post some raw data.