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Physics Fundamentals

Free Fall
Race

Predict which object lands first.
Real drag physics. 8 challenges.

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🏁 Kinematics Game

Free Fall Race — Free Online Terminal Velocity & Drag Force Game

Free Fall Race is a prediction game — make your call about which object lands first, then watch the real physics play out. Each object's motion is governed by F = ma with drag force F_d = ½ρC_dAv² applied every frame.

The physics behind the game

Free fall in vacuum

a = g = 9.8 m/s² for ALL objects

With no air resistance, every object accelerates identically. A feather and a cannonball hit the ground at the same time — Galileo proved this, Apollo 15 demonstrated it on the Moon.

Drag force

F_d = ½ρC_dAv²

Air resistance grows with the square of velocity. Once drag force equals weight, acceleration reaches zero — this is terminal velocity. Bigger cross-section and higher drag coefficient both increase drag.

Terminal velocity

v_t = √(2mg / ρC_dA)

The maximum speed of a falling object. Heavy objects and small cross-sections give high terminal velocity. Light objects with large cross-sections (like a parachute) have very low terminal velocity.

Stokes' drag (slow flow)

F_d = 6πηrv

For very slow flows or small objects (like dust particles, fog droplets), drag is proportional to velocity not velocity squared. This is Stokes' law.

Free Fall, Air Resistance, and Terminal Velocity

Free Fall Equations

In vacuum, all objects accelerate at g = 9.8 m/s² downward regardless of mass (equivalence principle). From rest: v = gt, s = ½gt², v² = 2gs. From non-zero initial velocity: use SUVAT with a = g downward. Apollo 15 astronaut David Scott demonstrated this on the Moon in 1971, dropping a hammer and feather simultaneously — they landed together in the 1.62 m/s² lunar gravity.

Air Resistance: F_d = ½ρC_dAv²

Drag force F_d = ½ρC_dAv²: ρ = air density (≈1.2 kg/m³ at sea level), C_d = drag coefficient (depends on shape: sphere ≈0.47, streamlined ≈0.04), A = cross-sectional area. Drag scales as v² — doubling speed quadruples drag. Net acceleration: a = g − F_d/m = g − (ρC_dA/2m)v². As v increases, a decreases, approaching zero at terminal velocity.

Terminal Velocity: v_t = √(2mg/ρC_dA)

When drag equals weight (F_d = mg): v_t = √(2mg/(ρC_dA)). v_t ∝ √(m/A): heavier or more streamlined objects fall faster. Skydiver spread-eagle: ~55 m/s (200 km/h). Head-down: ~90 m/s. With parachute (A ≈ 50 m²): ~4–6 m/s. Raindrops: 2–9 m/s. Without air resistance, a raindrop from 2 km altitude would reach ~198 m/s — the size of a rifle bullet. Air resistance keeps precipitation gentle.

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