Why "Time Up Equals Time Down" Isn't a Law of Physics

Ask any Class XI student what happens to the time a ball takes to rise compared to the time it takes to fall back down, and you’ll get the answer instantly: they’re equal. It’s one of the first “facts” taught in projectile motion, used constantly to halve the time of flight formula, to simplify problems, and to sanity-check answers.

It is also not a law of physics. It’s a consequence of one specific assumption most students never see stated out loud: that the object lands at the same height it was launched from.

Where the symmetry actually comes from

Vertical position under gravity is y(t) = v₀ sinθ · t − ½gt², a downward-opening parabola in t. A parabola is symmetric about its vertex, which is exactly the moment of maximum height. If the object starts and ends at y = 0, those two points sit symmetrically around that vertex, so the two time intervals either side of it are identical by simple geometry alone, not by any deeper physical necessity.

Change one condition: launch from a cliff, a building, or even a table top, and y starts at some height y₀ > 0 and ends at y = 0. The parabola is no longer symmetric about that landing point. The object spends measurably longer falling than it did rising, because it has further to fall. The standard formula T = 2v₀sinθ/g silently assumes away this case. Using it anyway is the single most common projectile-motion mistake in board exams that involve a height difference.

What to do instead

When launch and landing heights differ, go back to the actual equation and solve the full quadratic y₀ + v₀sinθ·t − ½gt² = 0 for t. There are two roots; for a projectile launched upward from a height, only the positive one after the peak is physical. This isn’t harder physics, it’s the same equation, just without the shortcut that only works in the special case most textbooks quietly assume by default.

The same reasoning is why maximum range at 45° is also conditional rather than universal, which is covered in full on the Motion in a Plane page, with a simulation you can push past the special case yourself.