# Terminal Velocity Equation

by Jamez
Tags: equation, terminal, velocity
 P: 599 Terminal Velocity Equation A falling object on earth is subjected to a downward force $F_g=mg$, while it's air resitance constitutes an upward force often modelled by $$F_w=\frac{1}{2}C_D \rho A_F v^2$$. With $C_D$ a constant (drag coefficient) that models how aerodynamic the object is, for most object of the order 1 (for a raindrop for example ~0,5), $\rho$ the air density, $A_F$ the frontal area of the object (perpendicular to the direction of motion), and $v$ the velocity of the object. At terminal velocity the force on the object is zero (otherwise the object would accellerate!) so you can equate both force-equations yielding: $$mg=\frac{1}{2}C_D \rho A_F v^2$$ $$v=\sqrt{\frac{2mg}{C_D \rho A_F}}$$