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https://texercises.com/exercise/escaping-rocket/
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Exercise:
Escape velocity from the Earth is vO. What would be the percent decrease in length of a ft long Saturn V rocket traveling at that speed? One foot is .cm one mile is .m.

Solution:
SolQtyg/sqrt-vX^/nccX^ SolQtygmgX- SolQtyvc.*vX^/nccX^ The Lorentz factor corresponding to escape velocity is gamma fracsqrt-fracv^c^ g what is not accurate enough. A normal pocket calculator can compute gamma - gm though; if not one could use the approximate formulas for the Lorentz factor: gamma + frac fracv^c^ + vc gamma- frac fracv^c^ vc The change in length is Delta ell ell - ell_ whereas the new length is Lorentz contracted ell fracell_gamma The percentual change in the length hence is: fracDelta ellell_ fracell-ell_ell_ fracfracell_gamma-ell_ell_ fracgamma- gamma- frac fracv^c^ vc
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Exercise:
Escape velocity from the Earth is vO. What would be the percent decrease in length of a ft long Saturn V rocket traveling at that speed? One foot is .cm one mile is .m.

Solution:
SolQtyg/sqrt-vX^/nccX^ SolQtygmgX- SolQtyvc.*vX^/nccX^ The Lorentz factor corresponding to escape velocity is gamma fracsqrt-fracv^c^ g what is not accurate enough. A normal pocket calculator can compute gamma - gm though; if not one could use the approximate formulas for the Lorentz factor: gamma + frac fracv^c^ + vc gamma- frac fracv^c^ vc The change in length is Delta ell ell - ell_ whereas the new length is Lorentz contracted ell fracell_gamma The percentual change in the length hence is: fracDelta ellell_ fracell-ell_ell_ fracfracell_gamma-ell_ell_ fracgamma- gamma- frac fracv^c^ vc
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Tags
contraction, einstein, escaping, length, physics, relativity, rocket, srt
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Difficulty
(3, default)
Points
4 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator uz
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Link