Terminal velocity (derivations)

Derivations from Terminal velocity.

Derivation of Terminal Velocity

A falling object experiences two forces: gravitational force, and a large-velocity drag force. The addition of these two forces results in:

:$F\; =\; m\; g\; -\; q\; A\; C\_d\; ,$where:"m" is mass of the object:"g" is the acceleration due to gravity:"q" is $frac\{1\}\{2\}\; ho\; V^2$, which is commonly known as the dynamic pressure, where::"$ho$" is the fluid density (e.g. density of air)::"$V$" is the fluid (or air) velocity:"A" is the cross-sectional area of the object:"$C\_d$" is the drag coefficient of the falling object

The terminal velocity is reached when $F\; =\; 0$, so:$m\; g\; -\; q\; A\; C\_d\; =\; 0\; =\; m\; g\; -\; frac\{1\}\{2\}\; ho\; V^2\; A\; C\_d$.Solving for $V$ to obtain the expression for terminal velocity,:$V\_t\; =\; sqrt\{\; frac\{2mg\}\{\; ho\; A\; C\_d\}\; \}$