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

Revision as of 14:01, 8 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.

Statements

instance of

Mathematical Formulation

0 references

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}}

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

\rho

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

Generalizes Formulation

Free Fall Equation (Vacuum)

Mathematical Condition

Q4011 (Deleted Item)

Vanishing Drag Coefficient

0 references

Identifiers

Wikidata QID

Q38083707

0 references

@@ Property / in defining formula @@
+ $v$ 
v
@@ Property / in defining formula: $v$ / rank @@
+Normal rank
@@ Property / in defining formula: $v$ / qualifier @@
+symbol represents: Free Fall Velocity
@@ Property / in defining formula @@
+ $m$ 
m
@@ Property / in defining formula: $m$ / rank @@
+Normal rank
@@ Property / in defining formula: $m$ / qualifier @@
+symbol represents: Free Fall Mass
@@ Property / in defining formula @@
+ $g$ 
g
@@ Property / in defining formula: $g$ / rank @@
+Normal rank
@@ Property / in defining formula: $g$ / qualifier @@
+symbol represents: Gravitational Acceleration
@@ Property / in defining formula @@
+ $\rho$ 
\rho
@@ Property / in defining formula: $\rho$ / rank @@
+Normal rank
@@ Property / in defining formula: $\rho$ / qualifier @@
+symbol represents: Density of Air
@@ Property / in defining formula @@
+ $C_{D}$ 
C_D
@@ Property / in defining formula: $C_{D}$ / rank @@
+Normal rank
@@ Property / in defining formula: $C_{D}$ / qualifier @@
+symbol represents: Drag Coefficient
@@ Property / in defining formula @@
+ $A$ 
A
@@ Property / in defining formula: $A$ / rank @@
+Normal rank
@@ Property / in defining formula: $A$ / qualifier @@
+symbol represents: Cross Section
@@ Property / in defining formula @@
+ $v_{0}$ 
v_0
@@ Property / in defining formula: $v_{0}$ / rank @@
+Normal rank
@@ Property / in defining formula: $v_{0}$ / qualifier @@
+symbol represents: Free Fall Initial Velocity
@@ 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 @@
+ $y$ 
y
@@ Property / in defining formula: $y$ / rank @@
+Normal rank
@@ Property / in defining formula: $y$ / qualifier @@
+symbol represents: Free Fall Height
@@ 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 / 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: Q4011 (Deleted Item)
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
+Mathematical Condition: Vanishing Drag Coefficient

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

$v$

$m$

$g$

$\rho$

$C_{D}$

$A$

$v_{0}$

$v_{\infty }$

$t$

$y$

$y_{0}$

Revision as of 14:01, 8 October 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

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

v {\displaystyle v}

m {\displaystyle m}

g {\displaystyle g}

ρ {\displaystyle \rho }

C D {\displaystyle C_{D}}

A {\displaystyle A}

v 0 {\displaystyle v_{0}}

v ∞ {\displaystyle v_{\infty }}

t {\displaystyle t}

y {\displaystyle y}

y 0 {\displaystyle y_{0}}

Revision as of 14:01, 8 October 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

$v$

$m$

$g$

$\rho$

$C_{D}$

$A$

$v_{0}$

$v_{\infty }$

$t$

$y$

$y_{0}$