Free fall describes the simplest form of gravitational motion: an object moving under gravity alone, with no other forces acting on it. Galileo overturned 2,000 years of Aristotelian thinking when he showed that all objects fall at the same rate regardless of mass. Today, the SUVAT equations derived from this principle underlie everything from safety engineering to space mission planning.
Galileo's Discovery — All Objects Fall Equally
Aristotle believed heavy objects fall faster than light ones — a view that persisted for nearly two millennia. Galileo overturned it by logical argument and experiment. If a heavy stone falls faster, he reasoned, then tying a light stone to a heavy one should slow the heavy one (the light stone holding it back) but also speed up the light one. The result cannot be both faster and slower than the heavy stone alone — a contradiction. Therefore, all objects must fall at the same rate. Galileo confirmed this by rolling balls down inclined planes (slowing gravity to measure it) and, according to legend, dropping weights from the Leaning Tower of Pisa. The Apollo 15 mission provided the definitive demonstration in 1971: astronaut David Scott dropped a hammer and a feather simultaneously on the airless Moon, and both hit the ground at exactly the same moment. This equivalence of gravitational and inertial mass is now a cornerstone of general relativity.
The Free Fall Equations
Free fall from rest (initial velocity u = 0) under constant gravitational acceleration g obeys the SUVAT equations simplified to: height fallen h = ½gt²; fall time t = √(2h/g); impact velocity v = gt = √(2gh); and kinetic energy at impact KE = ½mv² = mgh (exactly equal to the gravitational potential energy lost). On Earth, g = 9.807 m/s², so an object falls 4.9 m in the first second, 19.6 m in the second second, and 44.1 m in the first three seconds combined — each successive second covers more ground as velocity accumulates. After 1 s: 9.8 m/s; after 2 s: 19.6 m/s; after 3 s: 29.4 m/s. These equations also apply in reverse to projectile motion — a ball thrown upward at v₀ decelerates at 9.807 m/s², reaches zero velocity at peak height h_max = v₀²/(2g), then falls back under the same free-fall equations. The symmetry is exact: the ball returns to the launch height with exactly the same speed v₀, regardless of how high it went, and total flight time is exactly 2 × (v₀/g). Air resistance breaks this symmetry, causing the ball to return more slowly than it left.
Terminal Velocity and Air Resistance
In reality, falling objects encounter air resistance — a drag force proportional to v² for most everyday speeds. As velocity increases, drag grows until it exactly equals gravitational force (mg), at which point net acceleration becomes zero and the object falls at constant terminal velocity: v_t = √(2mg / ρC_dA), where ρ is air density (1.225 kg/m³ at sea level), C_d is the drag coefficient, and A is the cross-sectional area facing the airflow. A skydiver in spread-eagle position (C_d ≈ 1.0, A ≈ 0.9 m²) of 80 kg reaches about 55 m/s (195 km/h). Switching to a head-down dive (A ≈ 0.25 m²) raises terminal velocity to roughly 75 m/s (270 km/h). A raindrop reaches only about 9 m/s because it is small and approximately spherical (low drag area relative to weight). Hailstones, being denser and larger, can reach 40 m/s and cause substantial damage. A steel ball bearing reaches much higher terminal velocity than a feather of the same size because its greater mass-to-area ratio (m/A) dominates the terminal velocity formula. If Earth had no atmosphere, a skydiver falling 4,000 m would reach over 280 m/s — far beyond any survivable impact velocity.
Gravity on Other Planets
Surface gravity varies with a planet's mass and radius via g = GM/R². Mars (g = 3.721 m/s²) has 37.9% of Earth's gravity, so an object dropped from 10 m takes √(20/3.721) = 2.32 s to reach the ground, versus 1.43 s on Earth. The Moon (g = 1.62 m/s²) extends the same fall to 3.51 s. Jupiter (g = 24.79 m/s²) compresses it to just 0.90 s, with an impact velocity of 22.4 m/s versus Earth's 14.0 m/s. These differences critically affect spacecraft design: Mars descent vehicles use a combination of a heat shield, supersonic parachutes, and retrorockets because Mars air is only 1% as dense as Earth's, making parachute-only landings insufficient. The Mars Science Laboratory (Curiosity) used a sky crane — a rocket-powered hovering platform — to lower the rover gently to the surface. Saturn's moon Titan (g = 1.35 m/s², dense nitrogen atmosphere) allowed the Huygens probe to descend on a simple parachute for 72 minutes, covering 170 km of altitude. Each planetary body's unique combination of gravity and atmospheric density demands a completely different landing architecture.
Free Fall in Everyday Safety Engineering
Free fall equations appear throughout workplace and structural safety engineering. A person falling from a 2-meter ladder reaches impact at v = √(2 × 9.807 × 2) ≈ 6.3 m/s (22.6 km/h) — enough to cause serious head injuries. A fall from 10 m produces v ≈ 14 m/s (50 km/h), with kinetic energy equivalent to being hit by a car. Fall arrest systems — safety harnesses, airbags, crash mats — are designed to extend the stopping distance and reduce peak deceleration. If an 80 kg worker is stopped from 14 m/s in 0.2 m (rigid barrier), deceleration = v²/(2s) = 196/0.4 = 490 m/s² = 50 g — potentially fatal. A well-designed fall arrest system extending the stop to 1.5 m reduces that to about 6.5 g — survivable but still injurious. OSHA mandates fall protection for workers at 1.8 m (6 ft) above a lower level; EN 355 lanyards are certified to limit arrest force to 6 kN maximum. Stunt airbags for film productions are sized for 10–15 m falls, decompressing over 1–2 m to keep peak deceleration below 10 g. Every height threshold in safety codes traces back to free-fall impact calculations combined with human injury tolerance data.