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How long does it take for a ball to fall to the bottom of a cone

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Definitely not a homework question here, just a game that friends and I try to play to guess how long it takes a ball to fall to the bottom of a cone.

I do not have a lot of physics experience, but I was under the impression that if we knew certain constants such as: the diameter and height of the cone, the mass of the ball, the velocity of the ball as it falls into the cone, the angle of the side of the cone, and the usual constants for gravity and friction – that we should be able to know the exact time the ball will fall to the bottom.

We should also be able to know the distance the ball travelled going around the cone before hitting the bottom.

Sadly, I am not quite able to work out how to guess either the time or distance.  Any suggestions?

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