Well, till now we have two sorts of suggestions to measure the distance. One, that could be called “direct” method (suggested by Yurek and Jaegoor), uses a tape, wheel or rope to measure. Other, that could be called “comparative” method (suggested by Ulrica and me), estimates the distance from the slinger position comparing dimensions. The first one is more accurate but needs more time of video. The second one, being shorter, may be less accurate (though enough valid).
I think the easiest way to use the direct method is with a rope or cord of enough thickness to be seen in all its length in the video. So there is no need to buy tools like long tapes or measure wheels if you have not yet one. I like to imagine the process: the slinger walk to the target holding a stick of 50 cm (the target diameter). There is a rope stretched between the target and the shooting position. He checks up the target with the stick and walk back dragging the rope to the camera position. There he measure the stick and the rope (the rope can be folded several times to measure only a fold). Then the series of shots begin. The camera position and the zoom can be free.
The comparative method requires that the zoom adjustment and the distance from the camera to shooting position are fixed for all slingers. Also the heights of the target and camera to the floor are fixed. The camera must be not touched during the video (except initially as we shall see), which is easy to check up in the image. Suppose for example a camera-slinger distance of 5 m. and a height of the camera (lens) of 1 m. There will be a pole or stick at the slinger position of 2 m height that fill permanently the entire height of the image. The top of the target will be also at 2 m. height (the center will be at 1.75 m). If the top of the target in the video matches a height of 1.20 cm on the pole, height that will have previously marked on it, then the distance will certainly be of 20 meters. To clearly understand this calculation one can make a little drawing.
To check up these fixed positions of the target and the camera, you could proceed as follows: the video begins by zooming on the target as close as possible. There will be a common object close to it, like a beer can (empty if possible,

). The can may even be stuck on the target with plasticine, and possibly come away at first impact on the target. If its height is 12 cm then the target will measure approximately 4 cans. Likewise, the height of the base of the target on the ground should be three targets. After checking the target, zoom back to its fixed position, covering exactly the pole height, and remain there motionless for the entire video.
The height of the pole will be directly measured with a tape and the camera-pole distance also with a tape, attaching its end to the pole and extending the tape till the camera lens ( blurred fingers will occupy the entire image).
Procedure time is small as there are not need of walking to the target and its verifications can be made stopping the video (1 second of video on the target will be enough). Only the distance camera-pole would take 5 or 6 seconds.
If we don´t find another method we can use one of these. Which seems most appropiate?