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

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.

Statements

instance of

mathematical expression

0 references

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}}) \\ v (t) & = v_{\infty} \tanh (\frac{g t}{v_{\infty}}) \end{matrix}

has characteristic

nonlinearity

1 reference

described at URL

https://en.wikipedia.org/wiki/Free_fall

in defining formula

v

symbol represents

Free Fall Velocity

0 references

m

symbol represents

Free Fall Mass

0 references

g

symbol represents

Gravitational Acceleration

0 references

ρ

symbol represents

density of air

0 references

C_{D}

symbol represents

Drag Coefficient

0 references

A

symbol represents

Cross Section

0 references

v_{0}

symbol represents

Free Fall Initial Velocity

0 references

v_{\infty}

symbol represents

Free Fall Terminal Velocity

0 references

t

symbol represents

time

0 references

y

symbol represents

Free Fall Height

0 references

y_{0}

symbol represents

Free Fall Initial Height

0 references

community

MathModDB

0 references

described at URL

https://en.wikipedia.org/wiki/Free_fall

0 references

subclass of

Free Fall Equation (Non-Uniform Gravitation)

assumes

Uniform Gravitational Acceleration

0 references

Identifiers

Wikidata QID

Q38083707

0 references

@@ 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{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}
+ $\begin{matrix} m \dot{v} & = m g - \frac{1}{2} ρ C_{D} A v^{2} \\ y (t) & = y_{0} + v_{0} t - \frac{v_{\infty}^{2}}{g} \ln \cosh (\frac{g t}{v_{\infty}}) \\ v (t) & = v_{\infty} \tanh (\frac{g t}{v_{\infty}}) \end{matrix}$ 
\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}
@@ 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 @@
+ $v_{\infty}$ 
v_\infty
@@ Property / in defining formula: $v_{\infty}$ / rank @@
+Normal rank
@@ Property / in defining formula: $v_{\infty}$ / qualifier @@
+symbol represents: Free Fall Terminal Velocity
@@ Property / in defining formula @@
+ $t$ 
t
@@ Property / in defining formula: $t$ / rank @@
+Normal rank
@@ Property / in defining formula: $t$ / qualifier @@
+symbol represents: time
@@ 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 / community @@
+MathModDB
@@ Property / community: MathModDB / rank @@
+Normal rank
@@ 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

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

T4schmidt (talk | contribs)

$\begin{matrix} m \dot{v} & = m g - \frac{1}{2} ρ C_{D} A v^{2} \\ y (t) & = y_{0} + v_{0} t - \frac{v_{\infty}^{2}}{g} \ln \cosh (\frac{g t}{v_{\infty}}) \end{matrix}$

$\begin{matrix} m \dot{v} & = m g - \frac{1}{2} ρ C_{D} A v^{2} \\ y (t) & = y_{0} + v_{0} t - \frac{v_{\infty}^{2}}{g} \ln \cosh (\frac{g t}{v_{\infty}}) \\ v (t) & = v_{\infty} \tanh (\frac{g t}{v_{\infty}}) \end{matrix}$

$v_{\infty}$

$t$

$y_{0}$

Latest revision as of 16:54, 4 December 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

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

T4schmidt (talk | contribs)

mv˙=mg−12ρCDAv2y(t)=y0+v0t−v∞2gln⁡cosh⁡(gtv∞)

mv˙=mg−12ρCDAv2y(t)=y0+v0t−v∞2gln⁡cosh⁡(gtv∞)v(t)=v∞tanh⁡(gtv∞)

v∞

t

y0

Latest revision as of 16:54, 4 December 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

$\begin{matrix} m \dot{v} & = m g - \frac{1}{2} ρ C_{D} A v^{2} \\ y (t) & = y_{0} + v_{0} t - \frac{v_{\infty}^{2}}{g} \ln \cosh (\frac{g t}{v_{\infty}}) \end{matrix}$

$\begin{matrix} m \dot{v} & = m g - \frac{1}{2} ρ C_{D} A v^{2} \\ y (t) & = y_{0} + v_{0} t - \frac{v_{\infty}^{2}}{g} \ln \cosh (\frac{g t}{v_{\infty}}) \\ v (t) & = v_{\infty} \tanh (\frac{g t}{v_{\infty}}) \end{matrix}$

$v_{\infty}$

$t$

$y_{0}$