Drop a feather and a hammer in air: the hammer wins easily. Drop them in a vacuum: they land simultaneously. This demonstration — performed on the Moon by Apollo 15 astronaut David Scott in 1971 — reveals one of the most profound truths in physics: in the absence of air resistance, all objects fall with the same acceleration. This is free fall. The feather's different behaviour in air is explained by terminal velocity — the constant speed reached when drag equals gravity.
Free fall is motion under gravity alone, with no other forces acting (no air resistance). Every object in free fall near Earth's surface accelerates at g = 9.8 m/s² downward, regardless of mass. Motion is described by SUVAT equations with a = g.
Free Fall: g = 9.8 m/s²
Every second of free fall adds 9.8 m/s of downward speed. Distance from rest: s = ½gt² — quadratic, not linear. The first metre of a fall takes longer than the last.
| Time (s) | Speed (m/s) | Distance fallen (m) |
|---|---|---|
| 1 | 9.8 | 4.9 |
| 2 | 19.6 | 19.6 |
| 3 | 29.4 | 44.1 |
| 4 | 39.2 | 78.4 |
Why All Objects Fall at the Same Rate
By Newton's second law: a = F/m = mg/m = g. Mass cancels exactly. A heavier object has more gravitational force pulling it down, but also proportionally more inertia resisting acceleration — the two effects cancel. This cancellation, between gravitational mass and inertial mass, is one of the most precisely verified facts in physics (tested to 1 part in 10¹²) and is the foundation of Einstein's general relativity via the equivalence principle.
Free Fall Worked Examples
Example 1: Ball dropped from rest
Dropped from 45 m. Time to hit ground, speed on impact:
Example 2: Ball thrown upward at 20 m/s
Total time for round trip: T = 2 × 2.04 = 4.08 s.
Air Resistance and Terminal Velocity
In air, drag opposes motion with magnitude approximately:
where ρ is air density (~1.2 kg/m³), C_d is drag coefficient (shape-dependent), A is cross-sectional area, and v is speed. As a falling object speeds up, drag increases until it equals weight — at that point net force is zero, acceleration is zero, and velocity is constant: terminal velocity.
| Object | Terminal velocity |
|---|---|
| Raindrop (2 mm) | ~9 m/s (32 km/h) |
| Human (spread-eagle) | ~55 m/s (200 km/h) |
| Human + open parachute | ~5–6 m/s (18–22 km/h) |
| Feather | ~0.5 m/s (1.8 km/h) |
A parachute dramatically increases C_d and A, reducing terminal velocity from ~55 m/s to ~5–6 m/s — a survivable landing speed. The feather's tiny mass with large relative area gives it terminal velocity < 1 m/s — it practically floats.
Diagram — Velocity vs time: free fall with and without air resistance
Frequently Asked Questions
What is free fall?
Free fall is motion under gravity alone — no air resistance or other forces. In free fall near Earth's surface every object accelerates at g = 9.8 m/s² downward regardless of mass. Distance fallen from rest: s = ½gt².
What is terminal velocity?
Terminal velocity is the constant speed reached when drag force equals weight — net force is zero, acceleration is zero. Formula: v_t = √(2mg / ρC_d A). A spread-eagle skydiver reaches ~55 m/s; with parachute open, ~5–6 m/s.
Why do all objects fall at the same rate in a vacuum?
Newton's second law: a = F/m = mg/m = g. Mass cancels — acceleration equals g for every object regardless of mass. In vacuum, with no drag force to differentiate objects by size and shape, all objects hit the ground at the same time when dropped from the same height.
How does a parachute reduce terminal velocity?
A parachute increases cross-sectional area A and drag coefficient C_d enormously. Since v_t = √(2mg / ρC_d A), increasing C_d A reduces terminal velocity dramatically — from ~55 m/s to ~5–6 m/s, making landing survivable.
What is the acceleration during free fall?
In true free fall: constant g = 9.8 m/s² downward throughout. With air resistance: starts at ~g and decreases as speed increases (drag increases), reaching zero at terminal velocity. The object then maintains constant speed.
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Written by
Dr. Marcus WebbTheoretical physicist and science communicator with a PhD from Caltech. Research background in classical mechanics and gravitational physics. Passionate about making advanced physics accessible to all learners.
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