Terminal Velocity of a Falling Body
Terminal Velocity of a Falling Body
A falling body stops accelerating once drag equals weight; that balance speed is its terminal velocity.
Setting drag equal to weight gives v_t = √(2mg/(ρ·C_d·A)). where m is the mass, g gravity, ρ the fluid density, C_d the drag coefficient and A the frontal area.
Inputs
m := 80 kg=80 kg
g := 9.81 m/s^2=9.81 m/s^2
rho := 1.225 kg/m^3=1.23 kg/m^3
C_d := 1.0=1
A := 0.7 m^2=0.7 m^2
Solve the weight–drag balance for velocity.
v_t := sqrt((2·m·g)/(rho·C_d·A))=42.78 m/s
Results
The terminal velocity rises with the square root of mass and falls with frontal area — which is why a parachute, with its huge area, brings the speed right down.
Assumptions & limitations
- Constant drag coefficient.
- Reached steady state (no acceleration).
- Uniform fluid density.