Projectile motion

The single idea that unlocks projectile motion is that horizontal and vertical motion do not interact at all. Gravity pulls straight down, so it accelerates the vertical motion and has nothing whatsoever to say about the horizontal — no horizontal force means no horizontal acceleration, so horizontal velocity stays exactly constant for the whole flight, whether the projectile is rising, at its peak, or falling.

That independence is what makes the classic demonstration work: a ball thrown horizontally off a table and a ball simply dropped from the same height, released at the same instant, hit the floor at exactly the same time. The thrown ball's horizontal motion is real — it travels far sideways before landing — but that sideways travel does not slow down or speed up its fall in any way, because falling is governed entirely by the vertical component, which is identical for both balls: both start with zero vertical velocity and accelerate downward at g.

At the peak of an angled trajectory it is only the vertical velocity that reaches zero, for a moment, before reversing sign. The horizontal velocity is completely unaffected and is not zero there — the projectile is still moving sideways at exactly the same speed it started with, which is why the trajectory is not symmetric in speed but is symmetric in shape: the path up mirrors the path down, and (on level ground) the time to rise equals the time to fall, because both are governed by the same constant vertical deceleration and acceleration.