And the answer is:

>! Surprisingly, it's 1, that is, it's the same as if nothing happens when the ants collide, and this doesn't depend on $n$.

Explanation:

>! The phrase that says you're watching a particular ant is just a distraction so that people will think that there is complexity in this riddle, while in fact it's very simple. When two ants collide and each reverses its direction, position-wise it's the same as if each ant simply continues moving in the original direction. So the maximum time is when there is an ant at on end of a stick facing the other end. Since the maximum time an ant can be in the stick is 1 (from one end to the other), therefore by time 1 all ants will already fall off the stick, including the particular ant that you're watching.

Alternative explanation:

>! Imagine that **each ant holds a number**, and when two ants collide (and reverse their directions), they will **exchange the number**. Now the crucial observation is: **the numbers will never change its direction**. So the maximum time a number can be on the stick is 1 (the numbers are always moving on the same direction with the same speed). So by the time 1, all numbers will have fallen down. Since every number is held by an ant, when there is no number, there is no ant either. Therefore by the time 1, all ants will have already fallen from the stick, including the particular ant you are watching.