Question: I was once asked the following question by a student I was tutoring; and I was stumped by it:

When one throws a stone why does it take the same amount of time for a stone to rise to its peak and then down to the ground?

* One could say that this is an experimental observation; after one could envisage, hypothetically, where this is not the case.
* One could say that the curve that the stone describes is a parabola; and the two halves are symmetric around the perpendicular line through its apex. But surely the description of the motion of a projectile as a parabola was the outcome of observation; and even if it moves along a parabola, it may (putting observation aside) move along it with its descent speed different from its ascent; or varying; and this, in part, leads to the observation or is justified by the Newtons description of time - it flows equably everywhere.
* It's because of the nature of the force. It's independent of the motion of the stone.

I prefer the last explanation - but is it true? And is this the best explanation?

Answer: 
I think its because both halves of a projectile's trajectory are symmetric in every aspect. The projectile going from its apex position to the ground is just the time reversed version of the projectile going from its initial position to the apex position.
Conservation of momentum!
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### Force × Time = Impulse = Δ Momentum

Since the average force is the same going up and down, and since the momentum change is the same going up and down as well, the time during which the force is applied must also be the same.