# Difference between revisions of "Parabolic Shot/es"

(Created page with "ESTA PÁGINA ESTÁ SIENDO TRADUCIDA. TEN UN POCO DE PACIENCIA. GRACIAS.") |
|||

Line 1: | Line 1: | ||

ESTA PÁGINA ESTÁ SIENDO TRADUCIDA. TEN UN POCO DE PACIENCIA. GRACIAS. | ESTA PÁGINA ESTÁ SIENDO TRADUCIDA. TEN UN POCO DE PACIENCIA. GRACIAS. | ||

+ | == Mathematical function to follow == | ||

+ | |||

+ | We're going to simulate a cannon shot. A cannonball describes a parabolic trajectory after it is fired from the cannon. | ||

+ | |||

+ | {{l|Image:Parabolic-shot.gif}} | ||

+ | |||

+ | The mathematical equations that govern the trajectory are: | ||

+ | |||

+ | <math>X(t)=V_{0x}\cdot t+X_0</math> | ||

+ | |||

+ | <math>Y(t)=-\frac{1}{2}\cdot G \cdot t^2 + V_{0y}\cdot t + Y_0</math> | ||

+ | |||

+ | where: | ||

+ | |||

+ | <math>t</math> = the current time for the mathematical equation. | ||

+ | |||

+ | <math>X</math> = the 'x' coordinate of the bullet at a time 't' | ||

+ | |||

+ | <math>Y</math> = the 'y' coordinate of the bullet at a time 't' | ||

+ | |||

+ | <math>X_0</math> = the 'x' position of the bullet at time t = 0 | ||

+ | |||

+ | <math>Y_0</math> = the 'y' position of the bullet at time t = 0 | ||

+ | |||

+ | <math>V_{0x}</math> = the 'x' component of the velocity when shot (t = 0) | ||

+ | |||

+ | <math>V_{0y}</math> = the 'y' component of the velocity when shot (t = 0) | ||

+ | |||

+ | <math>G</math> = the gravity's acceleration. | ||

+ | |||

+ | You usually have the angle and the velocity modulus instead of its components. The decomposition is quite easy: | ||

+ | |||

+ | <math>V_{0x} = V_0 \cdot \cos \varphi</math> | ||

+ | |||

+ | <math>V_{0y} = V_0 \cdot \sin \varphi</math> | ||

+ | |||

+ | where: | ||

+ | |||

+ | <math>V_0</math> = the velocity when shot (t = 0) | ||

+ | |||

+ | <math>\varphi</math> = the cannon shooting angle with the horizontal. | ||

+ | |||

+ | See [http://en.wikipedia.org/wiki/Trajectory_of_a_projectile this Wikipedia article] if you need more information regarding the maths equations of a parabolic shot. |

## Revision as of 10:53, 13 October 2011

Warning!
The release of Synfig Studio 0.64.0 introduced new terminology and this translated page needs to be updated according to original English text. You can help updating this page - see instructions here. Thank you! |

ESTA PÁGINA ESTÁ SIENDO TRADUCIDA. TEN UN POCO DE PACIENCIA. GRACIAS.

## Mathematical function to follow

We're going to simulate a cannon shot. A cannonball describes a parabolic trajectory after it is fired from the cannon.

The mathematical equations that govern the trajectory are:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle X(t)=V_{0x}\cdot t+X_0}**

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle Y(t)=-\frac{1}{2}\cdot G \cdot t^2 + V_{0y}\cdot t + Y_0}**

where:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle t}**
= the current time for the mathematical equation.

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle X}**
= the 'x' coordinate of the bullet at a time 't'

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle Y}**
= the 'y' coordinate of the bullet at a time 't'

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle X_0}**
= the 'x' position of the bullet at time t = 0

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle Y_0}**
= the 'y' position of the bullet at time t = 0

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{0x}}**
= the 'x' component of the velocity when shot (t = 0)

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{0y}}**
= the 'y' component of the velocity when shot (t = 0)

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle G}**
= the gravity's acceleration.

You usually have the angle and the velocity modulus instead of its components. The decomposition is quite easy:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{0x} = V_0 \cdot \cos \varphi}**

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{0y} = V_0 \cdot \sin \varphi}**

where:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_0}**
= the velocity when shot (t = 0)

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \varphi}**
= the cannon shooting angle with the horizontal.

See this Wikipedia article if you need more information regarding the maths equations of a parabolic shot.