Free Fall

The question

Drop a hammer and a feather from shoulder height and the hammer wins easily. But astronaut David Scott did exactly this on the Moon in 1971 — and they hit the dust at the very same instant. So is heavier really faster?

Strip away the air and every object — hammer, feather, even you — falls with the identical acceleration, g ≈ 9.8 m/s². It feels wrong because on Earth the air quietly cheats, holding back light, spread-out things. The real surprise runs deeper: gravity pulls HARDER on a heavier object, yet it still doesn't fall faster. Why that extra pull buys no extra speed is the whole lesson.

The key idea

Near Earth's surface every object in free fall accelerates downward at $g \approx 9.8\,\text{m/s}^2$, independent of its mass (when air resistance is negligible). Free fall is just constant-acceleration motion, so the SUVAT equations apply with $a = g$. Throwing straight up uses the same equations: the object decelerates, reaches $v = 0$ at the top, then accelerates back down — symmetrically.

Heavier objects feel a bigger gravitational force — but they also carry proportionally more inertia (resistance to being sped up), so the two effects cancel exactly and $a = F/m = g$ for everything. That is precisely why the violet and orange balls fell together in the vacuum sim. On Earth it is air resistance that breaks the tie, slowing light, spread-out objects like feathers until they coast at a constant 'terminal velocity' — remove the air, or use a dense compact object, and the tie returns. For any vertical motion, pick a positive direction and use the SUVAT equations with $a = g$: at the top of a throw $v = 0$ but a is still g (which is what turns the ball around), and by symmetry the object passes each height on the way down at the same speed it had going up. **Connect it:** the $g$ in $v = gt$ is $F = GM_Em/R_E^2$ divided by $m$ — free fall is gravitation's close-range limit, and the mass cancellation that makes all objects fall together is the same cancellation that makes orbits mass-independent. A projectile is this lesson plus a constant sideways velocity.

The formula

• ·Taking up as positive: u = initial velocity (m/s)
• ·v = velocity after time t (m/s)
• ·h = displacement from the start (m)
• ·g = 9.8 m/s²
• ·t = time (s). For a simple drop
• ·u = 0 and the object speeds up; for a throw-up
• ·u > 0 and gravity (−g) steadily reduces v until it reaches 0 at the peak
• ·then makes it negative on the way down.

What to remember

• ·In free fall every object accelerates at g ≈ 9.8 m/s² downward, whatever its mass.
• ·At the top of a throw the velocity is zero but the acceleration is still g downward.
• ·Rise and fall take equal times and reach equal speeds (symmetry).