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Maximum range of a projectile thrown from constant-speed circular motion

The problem of determining the angle at which a point mass launched from ground level with a given speed is a standard exercise in mechanics. Similar, yet conceptually and calculationally more difficult problems have been suggested to improve student proficiency in projectile motion. The problem of determining the maximum distance of a rock thrown from a rotating arm motion is presented and analyzed in detail in this text. The calculational results confirm several conceptually derived conclusions regarding the initial throw position and provide some details on the angles and the way of throwing (underhand or overhand) which produce the maximum throw distance.