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

Revision as of 15:05, 30 September 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 Formulation

0 references

in defining formula

v

symbol represents

Free Fall Velocity

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m

symbol represents

Free Fall Mass

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g

symbol represents

Gravitational Acceleration

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\rho

symbol represents

Density of Air

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C_{D}

symbol represents

Drag Coefficient

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A

symbol represents

Cross Section

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v_{0}

symbol represents

Free Fall Initial Velocity

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v_{\infty }

symbol represents

Free Fall Terminal Velocity

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y

symbol represents

Free Fall Height

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t

symbol represents

Time

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y_{0}

symbol represents

Free Fall Initial Height

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community

MathModDB

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P842 (Deleted Property)

0 Property P842 not found, cannot determine the data type to use.

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defining formula

m{\dot {v}}=mg-{\frac {1}{2}}\rho C_{D}Av^{2}

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y(t)=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)

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Generalizes Formulation

Free Fall Equation (Vacuum)

Vanishing Air Density

\rho \rightarrow 0

Vanishing Drag Coefficient

C_{D}\rightarrow 0

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Identifiers

Wikidata QID

Q38083707

0 references

@@ 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 / in defining formula @@
+ $y$ 
y
@@ Property / in defining formula: $y$ / rank @@
+Normal rank
@@ Property / in defining formula: $y$ / qualifier @@
+symbol represents: Free Fall Height
@@ 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 / 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

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

$\rho \rightarrow 0$

$C_{D}\rightarrow 0$

$y$

$t$

$y_{0}$

$y(t)=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)$

Revision as of 15:05, 30 September 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

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

ρ → 0 {\displaystyle \rho \rightarrow 0}

C D → 0 {\displaystyle C_{D}\rightarrow 0}

y {\displaystyle y}

t {\displaystyle t}

y 0 {\displaystyle y_{0}}

y ( t ) = y 0 + v 0 t − v ∞ 2 g ln ⁡ cosh ⁡ ( g t v ∞ ) {\displaystyle y(t)=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)}

Revision as of 15:05, 30 September 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

$\rho \rightarrow 0$

$C_{D}\rightarrow 0$

$y$

$t$

$y_{0}$

$y(t)=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)$