Exercise
https://texercises.com/exercise/velocity-at-alggi-alp/
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Älggi-Alp
Staycoolandbegood, , 2006, digital photograph, Wikipedia
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The following quantities appear in the problem: Geschwindigkeit \(v\) / Radius \(r\) / Winkelgeschwindigkeit / Kreisfrequenz \(\omega\) / Winkel \(\theta\) /
The following formulas must be used to solve the exercise: \(v = r \omega \quad \) \(\cos\alpha = \dfrac{b}{c} \quad \)
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Exercise:
The geographical centre of Switzerland has the coordinates ang;;N and ang;;E and is called Älggi-Alp. How fast does a person standing there travel around Earth's rotational axis?

Solution:
Skz center tikzpicture drawdashed ---; drawthick --. nodeabove N; drawthick ----. nodebelow S; filldrawcolorred fillred!!white --. arc :adX:.--cycle; nodecolorred at adX/:. gamma; draw--+adX: nodemidway left R; drawdotted colorblue ---; drawvery thick colorblue circlecm; coordinate R at adX:; coordinate O at ; drawcolorgreen!!black R-- R -| O nodemidway below r; tikzpicture center % Geg gamma ang;;N a T h pf omega w textErde rightarrow R RO R % GesGeschwindigkeitvsi % The distance of Älggi-Alp to the Earth's rotational axis is SolQtyrRX*cosaXm al r Rcosphi R cosa r. The velocity of an object rotating with the Earth around it's axis therefore is: SolQtyvwX*rX al v omega r omega Rcosphi w r v v omega Rcosphi v
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\(\LaTeX\)-Code
Exercise:
The geographical centre of Switzerland has the coordinates ang;;N and ang;;E and is called Älggi-Alp. How fast does a person standing there travel around Earth's rotational axis?

Solution:
Skz center tikzpicture drawdashed ---; drawthick --. nodeabove N; drawthick ----. nodebelow S; filldrawcolorred fillred!!white --. arc :adX:.--cycle; nodecolorred at adX/:. gamma; draw--+adX: nodemidway left R; drawdotted colorblue ---; drawvery thick colorblue circlecm; coordinate R at adX:; coordinate O at ; drawcolorgreen!!black R-- R -| O nodemidway below r; tikzpicture center % Geg gamma ang;;N a T h pf omega w textErde rightarrow R RO R % GesGeschwindigkeitvsi % The distance of Älggi-Alp to the Earth's rotational axis is SolQtyrRX*cosaXm al r Rcosphi R cosa r. The velocity of an object rotating with the Earth around it's axis therefore is: SolQtyvwX*rX al v omega r omega Rcosphi w r v v omega Rcosphi v
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Attributes & Decorations
Tags
circle, circular motion, mechanics, physics, switzerland, älggi
Content image
Älggi-Alp
Difficulty
(1, default)
Points
1 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator uz
Decoration
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Link