Terminal Velocity
Terminal Velocity
\[v_t = \sqrt{\frac{2mg}{\rho C_d A}}\]
Variables
vt = terminal velocity (m/s)
m = mass (kg)
g = gravitational acceleration (m/s²)
rho = fluid density (kg/m³)
Cd = drag coefficient
A = reference area (m²)
Description
What is this formula?
The terminal velocity equation calculates the constant maximum speed reached by a falling object when drag force equals gravitational force.
When to use it
Use this formula when analyzing falling objects, parachutes, atmospheric descent, rain droplets, or aerodynamic resistance problems.
Example
A skydiver with mass 80 kg falls through air with density 1.225 kg/m³, drag coefficient 1.0, and frontal area 0.7 m².
Data:
m = 80 kg
g = 9.81 m/s²
rho = 1.225 kg/m³
Cd = 1.0
A = 0.7 m²
Formula:
vt = √((2*m*g)/(rho*Cd*A))
Substitution:
vt = √((2*80*9.81)/(1.225*1.0*0.7))
Result:
vt ≈ 42.8 m/s
Applications
Parachute design, aerospace engineering, meteorology, sports science, atmospheric physics, and fluid mechanics.
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