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

← Older edit

@@ 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}
+Normal rank
+has characteristic: nonlinearity
@@ Property / in defining formula @@
+ $y_{0}$ 
y_0
@@ Property / in defining formula: $y_{0}$ / rank @@
+Normal rank
@@ Property / in defining formula: $y_{0}$ / qualifier @@
+symbol represents: Free Fall Initial Height
@@ Property / Wikidata QID @@
+Q38083707
@@ Property / Wikidata QID: Q38083707 / rank @@
+Normal rank
@@ Property / community @@
+MathModDB
@@ Property / community: MathModDB / rank @@
+Normal rank
@@ Property / Is Linear @@
+Amount 0
Unit 1
 Amount
 Unit
@@ Property / Is Linear: 0 / rank @@
+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 @@
+subject has role: Mathematical Formulation
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
+object has role: Mathematical Formulation
@@ 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

Latest revision as of 11:41, 2 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.