There are 40 identical balls travelling along a straight line on a smooth horizontal table. All balls have equal speed v and each one is travelling to right or left. All collisions between the balls is head on elastic. At some point in time all balls will have fallen off the table. The time at which this happens will definitely depend on initial positions of the balls. Over all possible initial positions of the balls, what is the longest amount of time that you would need to wait to ensure that the table has no more balls? Assume that length of the table is L.

Answer

`(L)/(v)`