Free Fall Equation (Air Drag)

Available identifiers

modeling the fall of objects by the laws of classical mechanics, including aerodynamic drag and assuming a uniform gravitational field

Moreover, assuming the falling object to be a point mass.

Defining Formula: $\begin{matrix} m \dot{v} & = & m g - \frac{1}{2} ρ C_{D} A v^{2} \\ v (t) & = & v_{0} + v_{\infty} \tanh (\frac{g t}{v_{\infty}}) \\ y (t) & = & y_{0} + v_{0} t - \frac{v_{\infty}^{2}}{g} \ln \cosh (\frac{g t}{v_{\infty}}) \end{matrix}$
$A$ symbol represents Cross Section
$C_{D}$ symbol represents Drag Coefficient
$ρ$ symbol represents Density of Air
$g$ symbol represents Gravitational Acceleration (Earth Surface)
$m$ symbol represents Free Fall Mass
$t$ symbol represents Time
$v$ symbol represents Free Fall Velocity
$v_{0}$ symbol represents Free Fall Initial Velocity
$v_{\infty}$ symbol represents Free Fall Terminal Velocity
$y$ symbol represents Free Fall Height
$y_{0}$ symbol represents Free Fall Initial Height

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