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

← Older edit

@@ Property / defining formula / Property / defining formula @@
- ${\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$ 
\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) \end{align}
+ ${\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\\v(t)&=v_{\infty }\tanh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$ 
\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}
+described at URL: https://en.wikipedia.org/wiki/Free_fall
@@ Property / P842 (Deleted Property) @@
-Amount 0
Unit 1
 Property P842 not found, cannot determine the data type to use.
 Amount
 Unit
-Normal rank
@@ Property / Generalizes @@
-Free Fall Equation (Vacuum)
@@ Property / Generalizes: Free Fall Equation (Vacuum) / rank @@
-Normal rank
@@ Property / Generalizes: Free Fall Equation (Vacuum) / qualifier @@
-object has role: Mathematical Formulation
@@ Property / Generalizes: Free Fall Equation (Vacuum) / qualifier @@
-Vanishing Air Density:  $\rho \rightarrow 0$ 
\rho \rightarrow 0
@@ Property / Generalizes: Free Fall Equation (Vacuum) / qualifier @@
-Vanishing Drag Coefficient:  $C_{D}\rightarrow 0$ 
C_D \rightarrow 0
@@ Property / Generalizes: Free Fall Equation (Vacuum) / qualifier @@
-subject has role: Mathematical Formulation
@@ Property / Generalizes Formulation / Property / Generalizes Formulation @@
-Free Fall Model (Vacuum)
+Free Fall Equation (Vacuum)
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
+Mathematical Condition: Vanishing Air Density
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
+Mathematical Condition: Vanishing Drag Coefficient

Latest revision as of 10:11, 10 October 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.