What is the required speed to successfully complete the spinning cylinder game?

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the hollow cylinder shown in fig 2.2 (see attachment) is free to rotate on a horizontal axis. one hole is cut in the side of the cylinder. the object of the game is to spin the cylinder so fast that the object dropped through the hole when it is in the uppermost position will fall through the same hole when it has rotated to the bottom position. if the diameter of the cylinder is .5 meters how fast must the hole be moving (hint: first calculate the time for the object to fall the appropriate distance, then use that result to determine the number of rad/s.) I get 2..45 rad/s but the book gets 1.6? Try it and see what you get. Thanks

Stevo
 
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Although I haven't see your attachments yet, you have to remember that the acceleration of the ball isn't constant (it temporarily becomes 0 when the cylinder is horizintal and is "g" when vertical).
Try to relate the distance traveled with the acceleration at some instant of time and the corresponding acceleration at that instant.
Hint: Use S = 0.5at^2, a = gsin(theta) where theta = ...

Can you go from here ?

Arun