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

← Older edit

@@ Property / defining formula / Property / defining formula @@
- $m{\dot {v}}=mg-{\frac {1}{2}}\rho C_{D}Av^{2}$ 
m\dot{v}=mg-\frac{1}{2}\rho C_DAv^2
+ ${\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\\v(t)&=v_{\infty }\tanh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$ 
\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}
+has characteristic: nonlinearity
+described at URL: https://en.wikipedia.org/wiki/Free_fall
@@ Property / defining formula @@
- $y(t)=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)$ 
y(t)=y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right)
-Normal rank
@@ 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 Formulation @@
-Free Fall Equation (Vacuum)
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / rank @@
-Normal rank
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
-Vanishing Air Density:  $\rho \rightarrow 0$ 
\rho \rightarrow 0
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
-Vanishing Drag Coefficient:  $C_{D}\rightarrow 0$ 
C_D \rightarrow 0
@@ Property / Generalizes Formulation @@
+Free Fall Equation (Vacuum)
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / rank @@
+Normal rank
@@ 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.