I suspect you are assuming that high fps cameras are a lot newer than they are based on the fact that movies were shot at 24 fps. That wasn’t really a technological limitation. Film as just expensive and 24 fps was good enough
In reality high speed photography and film goes back to the late 1800s and actually predates the use of photo finishes.
That said, the very first photo finishes would use a string or something that broke once something passed the finish line and triggered a camera. That was in the 1890s and by 1920 we were simply using film, you just start recording a bit before the finish and you are set.
In the 1930s the strip-film camera was introduced for photo finishes. A piece of film was pulled past a thin-slit-aperture in the opposite direction to the competitor’s movement, effectively photographing just the finish line continuously over time. The first piece of the racing object (nose, chest, toe, hoof) would appear at the finish line first and everything else would trail behind it across the photo.. So the horizontal axis of the photo image is _time_.
This gave weird distortions for slow moving parts of the racers, but the first part of the winner to cross the finish line would always be the “left-most” (or “right-most” depending on which side the image was taken from) thing in the photo.
The film was a long strip, not individual frames. The entire strip was dragged across the aperture, which was a slit positioned exactly on the finish line. When you develop it, it will show the finish line and anything that crosses it. Right to left you can see what crossed first. Anything not moving will be a streak, but anything that crosses the slit will show up as the object at the point where it crossed the line albeit slightly distorted.
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