Free Fall Equation (Air Drag) (Q3836): Difference between revisions

← Older edit

@@ Property / instance of / Property / instance of @@
-Q3832 (Deleted Item)
+mathematical expression
@@ Property / defining formula / Property / defining formula @@
- $\begin{matrix} m \dot{v} & = & m g - \frac{1}{2} ρ C_{D} A v^{2} \\ y (t) & = & y_{0} + v_{0} t - \frac{v_{\infty}^{2}}{g} \ln \cosh (\frac{g t}{v_{\infty}}) \end{matrix}$ 
\begin{aligned} m\dot{v}&=&mg-\frac{1}{2}\rho C_DAv^2 \\ y(t)&=&y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right) \end{aligned}
+ $\begin{matrix} m \dot{v} & = m g - \frac{1}{2} ρ C_{D} A v^{2} \\ y (t) & = y_{0} + v_{0} t - \frac{v_{\infty}^{2}}{g} \ln \cosh (\frac{g t}{v_{\infty}}) \\ v (t) & = v_{\infty} \tanh (\frac{g t}{v_{\infty}}) \end{matrix}$ 
\begin{align} m\dot{v}&=mg-\frac{1}{2}\rho C_DAv^2 \\ y(t)&=y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right)\\ v(t) &= v_{\infty}\tanh\left(\frac{gt}{v_{\infty}}\right) \end{align}
+has characteristic: nonlinearity
+described at URL: https://en.wikipedia.org/wiki/Free_fall
@@ Property / defining formula @@
- $y (t) = y_{0} + v_{0} t - \frac{v_{\infty}^{2}}{g} \ln \cosh (\frac{g t}{v_{\infty}})$ 
y(t)=y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right)
-Normal rank
@@ Property / in defining formula: $ρ$ / qualifier @@
+symbol represents: density of air
@@ Property / in defining formula: $ρ$ / qualifier @@
-symbol represents: Q3851 (Deleted Item)
@@ Property / in defining formula: $t$ / qualifier @@
+symbol represents: time
@@ Property / in defining formula: $t$ / qualifier @@
-symbol represents: Q3846 (Deleted Item)
@@ Property / P842 (Deleted Property) @@
-Amount 0
Unit 1
 Property P842 not found, cannot determine the data type to use.
 Amount
 Unit
-Normal rank
@@ Property / P853 (Deleted Property) @@
-The value is invalid and cannot be displayed. Property P853 not found, cannot determine the data type to use.
-Normal rank
-Vanishing Air Density:  $ρ \to 0$ 
\rho \rightarrow 0
-Vanishing Drag Coefficient:  $C_{D} \to 0$ 
C_D \rightarrow 0
@@ Property / described at URL @@
+https://en.wikipedia.org/wiki/Free_fall
@@ Property / described at URL: https://en.wikipedia.org/wiki/Free_fall / rank @@
+Normal rank
@@ Property / subclass of @@
+Free Fall Equation (Non-Uniform Gravitation)
@@ Property / subclass of: Free Fall Equation (Non-Uniform Gravitation) / rank @@
+Normal rank
+assumes: Uniform Gravitational Acceleration

Latest revision as of 16:54, 4 December 2024

Modeling the fall of objects by the laws of classical mechanics, including the aerodynamic drag and assuming a uniform gravitational field. Moreover, assuming the falling object to be a point mass.

Language	Label	Description	Also known as
English	Free Fall Equation (Air Drag)	Modeling the fall of objects by the laws of classical mechanics, including the aerodynamic drag and assuming a uniform gravitational field. Moreover, assuming the falling object to be a point mass.