Free Fall Time

Free fall: t = √(2h/g)

Once you ignore air resistance, how long something takes to hit the ground comes down to two things only: the height it starts from and gravity. That gives you t = √(2h/g), with g ≈ 9.81 m/s², and a final velocity of v = g·t = √(2gh). Drop something from h = 10 m and it lands after about 1.43 s, hitting at roughly 14 m/s. Notice that mass never shows up in the equation. That was the whole point of Galileo's demonstration at the Tower of Pisa, and Apollo 15 later proved it on the Moon by dropping a feather and a hammer side by side. Down here in actual air, drag keeps building until it cancels gravity, and the object stops speeding up. That ceiling is the terminal velocity, around 55 m/s for a skydiver lying belly-down, or close to 90 m/s if they go head-first.

Applications

It shows up in skydiving and base-jumping prep, in packaging drop tests (ISTA, ASTM), in the forensic work that reconstructs falls from height, in structural impact engineering, and even in ride design like Disney's Tower of Terror and the free-fall towers at fairs.

FAQ

Does a heavier object fall faster? Not in a vacuum, where everything falls at the same rate. In air it can look that way because light, spread-out things like a feather or a sheet of paper get held back by drag.

What is terminal velocity? It's the speed where air drag has grown enough to match gravity, so the object can't accelerate any further. A skydiver in the belly position tops out around 55 m/s, about 200 km/h.

Does this formula work on the Moon? It does, you just swap in g ≈ 1.62 m/s². That same 10 m drop now takes about 3.5 s, more than double the Earth time.