Difference between revisions of "Parabolic Shot/es"

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ESTA PÁGINA ESTÁ SIENDO TRADUCIDA. TEN UN POCO DE PACIENCIA. GRACIAS.
 
ESTA PÁGINA ESTÁ SIENDO TRADUCIDA. TEN UN POCO DE PACIENCIA. GRACIAS.
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== Mathematical function to follow ==
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We're going to simulate a cannon shot. A cannonball describes a parabolic trajectory after it is fired from the cannon.
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{{l|Image:Parabolic-shot.gif}}
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The mathematical equations that govern the trajectory are:
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<math>X(t)=V_{0x}\cdot t+X_0</math>
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<math>Y(t)=-\frac{1}{2}\cdot G \cdot t^2 + V_{0y}\cdot t + Y_0</math>
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where:
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<math>t</math> = the current time for the mathematical equation.
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<math>X</math> = the 'x' coordinate of the bullet at a time 't'
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<math>Y</math> = the 'y' coordinate of the bullet at a time 't'
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<math>X_0</math> = the 'x' position of the bullet at time t = 0
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<math>Y_0</math> = the 'y' position of the bullet at time t = 0
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<math>V_{0x}</math> = the 'x' component of the velocity when shot (t = 0)
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<math>V_{0y}</math> = the 'y' component of the velocity when shot (t = 0)
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<math>G</math> = the gravity's acceleration.
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You usually have the angle and the velocity modulus instead of its components. The decomposition is quite easy:
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<math>V_{0x} = V_0 \cdot \cos \varphi</math>
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<math>V_{0y} = V_0 \cdot \sin \varphi</math>
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where:
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<math>V_0</math> = the velocity when shot (t = 0)
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<math>\varphi</math> = the cannon shooting angle with the horizontal.
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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

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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.

Image:Parabolic-shot.gif

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.


Languages Language: 

English • español