A ball with a 1m diameter starting out in the middle of a 5 pointed star table (outer 5 points - 10m radius..... inner 5 points - 5m radius) has a starting angle of a random value from 0 to 360 degrees. The ball is now set loose and travels around the table.

Now how many sides on average will have been hit once the ball has travelled 1000m ? Also, where are the most likely points that the ball will end up?

To make things even more wonderfully confusing, the star rotates at an ever increasing speed of half a revolution for every 10 metres the ball has travelled. These speed increases are in incremental 'jumps'. Observe: 0 revolutions per 10 metres of ball travel: (when the ball has travelled 0 - 10 metres) 0.5 revolutions per 10 metres of ball travel: (when the ball has travelled 10 - 20 metres) 1.0 revolutions per 10 metres of ball travel: (when the ball has travelled 20 - 30 metres) 1.5 revolutions per 10 metres of ball travel: (when the ball has travelled 30 - 40 metres) etc. etc.

Now how many sides on average will have been hit once the ball has travelled 1000m ?

Posted (edited)

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A ball with a 1m diameter starting out in the middle of a 5 pointed star table (outer 5 points - 10m radius..... inner 5 points - 5m radius) has a starting angle of a random value from 0 to 360 degrees. The ball is now set loose and travels around the table.

Now how many sides on average will have been hit once the ball has travelled 1000m ?

Also, where are the most likely points that the ball will end up?

To make things even more wonderfully confusing, the star rotates at an ever increasing speed of half a revolution for every 10 metres the ball has travelled. These speed increases are in incremental 'jumps'. Observe:

0 revolutions per 10 metres of ball travel: (when the ball has travelled 0 - 10 metres)

0.5 revolutions per 10 metres of ball travel: (when the ball has travelled 10 - 20 metres)

1.0 revolutions per 10 metres of ball travel: (when the ball has travelled 20 - 30 metres)

1.5 revolutions per 10 metres of ball travel: (when the ball has travelled 30 - 40 metres)

etc. etc.

Now how many sides on average will have been hit once the ball has travelled 1000m ?

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