DesertPilot
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Mountain View, CA
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You might have problems with energy losses. Every bit of energy that went into deforming the plastic, making a loud noise, or making the target vibrate would get lost to the system and wouldn't get measured by the speedometer. And you wouldn't be able to use conservation of momentum for a system like this because some of the projectile's momentum would get transfered through the bearing system to the earth.
I still think a ballistic seems the best way to go. It might suffer from energy losses as well, but if could figure out a way to track the darn thing while it twisted and swung after getting hit by an off-center shot, you could use conservation of momentum to get the projectile speed.
NOTE: In theory, if you can measure the path of the hand and sling, you can figure out the timing information, projectile speed, etc., by measuring the speed of the slinger's hand at the moment of release. This might be well within the range of a cheapo sports radar gun. I keep promising to post the equations... someday. I've turned them into a PDF file, but I still haven't gotten around to scanning them in. Maybe over Thanksgiving...
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