Falling Object Calculator
Would a penny dropped from the Empire State Building kill you? (Spoiler: no!) This calculator models falling objects with air resistance to find terminal velocity, actual impact speed, and impact energy. Enter the object's mass, size, drag coefficient, and drop height to see how physics saves you from falling pennies.
How We Calculate This
Terminal velocity: Vt = √(2mg/(ρACd)), where m=mass, g=9.80665 m/s², ρ=1.225 kg/m³ (sea level air), A=πr² (cross-section), Cd=drag coefficient. Fall time and impact speed use numerical integration of v(t) = Vt × tanh(gt/Vt).
Frequently Asked Questions
What is terminal velocity?
Terminal velocity is the constant speed a falling object reaches when air resistance equals gravitational force. At this speed, the object stops accelerating and falls at a constant rate.
Would a penny dropped from the Empire State Building kill you?
No! A penny's flat shape gives it high drag, limiting terminal velocity to about 40-65 km/h (depending on tumbling). It would sting but wouldn't cause serious injury. The penny myth is busted!
What is the drag coefficient?
The drag coefficient (Cd) measures how aerodynamic an object is. A smooth sphere has Cd ≈ 0.47, while a flat disk perpendicular to flow has Cd ≈ 1.1. Shape matters more than size for drag.
Why doesn't the calculator match vacuum predictions?
In a vacuum, objects accelerate continuously at 9.8 m/s². With air resistance, drag force increases with velocity squared, eventually balancing gravity. Real falls are always slower than vacuum predictions.
Why do skydivers have different speeds?
Body position changes cross-sectional area and drag coefficient dramatically. Belly-down (spread eagle) has maximum drag (~55 m/s terminal), while head-down diving reduces it (~80+ m/s).
Related Calculators
You might also find these calculators helpful: Escape Velocity, and Speed Converter.