Determining the optimum launch angle of a projectile (for the greatest distance) is of great interest to athletes such as shotputters, as they want the projectile to travel as far as possible.
I conducted an experiment using a marble rolling down a rubber track to determine the optimum launch angle. My results (see the graph below) were inconclusive, but suggested an angle between 43 and 49° was optimum. The report is available here.
However, other sources (e.g. Lenz and Rappl 2010) have found that the optimum angle (taking air resistance into account) is 42° for a projectile. This optimum angle is further lowered to 37 to 38° when throwing a shotput, as the human body can impart a greater force to the shot when pushing forward, rather than upward.
There were plenty of errors in my experiment, which suggests further experimentation in this area may be required. Perhaps there was some interference from the Magnus effect, as the marble had topspin from rolling down the ramp. Using a different method to launch the projectile would avoid this effect. Perhaps a cannon?
Another interesting factor to test would be the weight of the projectile. What is the optimum weight? Light projectiles are hard to throw, but heavy ones are too. Alternatively, an analysis of the angle that athletes actually throw the shotput at could be informative. Grab some unwilling friends, a shotput or heavy rock, a camera, the free program Tracker (to analyse the film) and you’re set. Maybe you could graph the angle they released at against the distance of the throw.