Shutter lag of the XTi
Measurements by Luk at doc-diy.net show this camera has an average* 116mS lag without mirror lockup, and a 66mS lag with mirror lockup. Fast pinewood derby cars travel about 10 feet per second (3 m/s), leading to a 7-14" (18-36cm) travel time before the image is captured. While the camera would never be used for judging, this is long enough that the cars could switch leads between the finish and the image capture, leading to questions about which vehicle really won.
Another comment on photo.net suggested that particularly old batteries may contribute to shutter lag. Given that I purchased the camera shortly after release, and haven't purchased batteries since then, I did buy two new batteries just in case this was affecting the timing. I didn't test out the old batteries though once I received the new, and my initial testing wasn't useful for determining actual timing, so I cannot confirm these results.
* The variance is shown in a chart on that site. With mirror lockup the fastest was 65mS, most were 66mS, and the slowest was 72mS. Without mirror lockup the fastest was 115mS, most were at 116mS, and the slowest at 164mS.
Shutter lag measurements for a variety of cameras
Another site has collected information about shutter lag times with and without autofocus. With SLRs I'm not sure the autofocus times are useful anyway since the lens focus motor speed is the largest factor there, and it varies from lens to lens. Most appear to be in the 50-100mS range, but some cameras have times of less than 10mS. Nothing about mirror lockup, though - I expect some of the higher end SLRs should have a much better mirror lockup time than this camera, so there's more data to be collected. Also would be interesting to see a comparison of those SLRs with live view while in live view mode.
So I knew it wouldn't work, and when I ran the pinewood derby I just hooked the projector to an HD camera and shot the end of the track and finish line so everyone could view the finish regardless of their sightline to the track itself.
Afterwards I did hook the camera up and ran a few races, and the results were as expected - the cars showed up in the image about 14 inches (no mirror lockup) past the finish gate.
If I wanted to use this camera in a future race, I would make a light beam trigger about 14 inches before the finish gate. A more advanced trigger would use mirror lockup about 2-3 feet before the gate, and another trigger about 8 inches before the gate. Even more advanced would involve a microcontroller (arduino or similar) and perform the mirror lockup at race start, measure the speed of the lead car about 12 inches prior to the gate, then trigger it based on the speed to capture the most likely point where they cross the finish gate.
The track and arena aren't particularly well lit, though, so another possibility is to use the same techniques as other high speed photographers. Set the camera to a low ISO and tight aperture, start a bulb exposure shortly before the gate, then use bright flashes triggered by the gate to illuminate the scene sufficiently to capture the intended image. This would be the most accurate, since the starting gate could then be used to trigger the flashes, and the image capture would happen absolutely simultaneously with the actual gate finish.
The video output of this camera is only composite (not component or HDMI - ie, an SD video image!) so it didn't look good anyway. I'd suggest, if someone later wants to do something like this, choose a camera with an HD output. It was usable and interesting, so I wouldn't drop money on a new camera just for this use, but it's yet another thing I'll have on my list of priorities when selecting my next camera.
Here are several of the images the camera captured. Again, this is without mirror lockup, being triggered at the gate in the photo.