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https://texercises.com/exercise/observing-meteor-from-rocket/
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Exercise:
An astronaut in a rocket traveling at .c with respect to Earth observes a meteor coming from behind and passing him at a speed he measures to be .c. How fast is the meteor moving with respect to earth?

Solution:
The speed of the meteor in his own mathcalS' frame is .c. The speed in the Earth frame mathcalS is therefore: u fracu'+v+fracvu'c^ frac.c+.c+frac.c .cc^ .c center tikzpicturescale. scope%Earth filldrawcolorblue fillblue!!white circle cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at .. mathcalS; scope scopescale. xshiftcm yshiftcm %flaps coordinate P at --; drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scoperotate around:Pshift-cm-cmyscalexscal drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scope %rocket drawfillred!!white -- tooutin - tooutin tooutin --; %peak drawfillblue!!white -. tooutin . tooutin tooutin -.; %central flap drawfillblue!!white - tooutin - - tooutin -; %porthole drawcolorgrayultra thickfillwhite!!blue -. circle .cm; %fuel foreach i in ... pgfmathsetmacroxrand*. + *- - . pgfmathsetmacroyrand*. + *.-. pgfmathsetmacroopacValrand*.+ drawcolorred fillred!!yellow xy circle .cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at mathcalS'; drawcolorred thick stealth - -- noderight v.c; scope scopescale xshift-cm yshift.cm filldrawcolorblack fillblack circle .cm; drawcolorred thickstealth- .-.--.-. noderight u?; drawcolorblue thickstealth- ..--.. noderight u'.c; scope tikzpicture center
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Exercise:
An astronaut in a rocket traveling at .c with respect to Earth observes a meteor coming from behind and passing him at a speed he measures to be .c. How fast is the meteor moving with respect to earth?

Solution:
The speed of the meteor in his own mathcalS' frame is .c. The speed in the Earth frame mathcalS is therefore: u fracu'+v+fracvu'c^ frac.c+.c+frac.c .cc^ .c center tikzpicturescale. scope%Earth filldrawcolorblue fillblue!!white circle cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at .. mathcalS; scope scopescale. xshiftcm yshiftcm %flaps coordinate P at --; drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scoperotate around:Pshift-cm-cmyscalexscal drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scope %rocket drawfillred!!white -- tooutin - tooutin tooutin --; %peak drawfillblue!!white -. tooutin . tooutin tooutin -.; %central flap drawfillblue!!white - tooutin - - tooutin -; %porthole drawcolorgrayultra thickfillwhite!!blue -. circle .cm; %fuel foreach i in ... pgfmathsetmacroxrand*. + *- - . pgfmathsetmacroyrand*. + *.-. pgfmathsetmacroopacValrand*.+ drawcolorred fillred!!yellow xy circle .cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at mathcalS'; drawcolorred thick stealth - -- noderight v.c; scope scopescale xshift-cm yshift.cm filldrawcolorblack fillblack circle .cm; drawcolorred thickstealth- .-.--.-. noderight u?; drawcolorblue thickstealth- ..--.. noderight u'.c; scope tikzpicture center
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Tags
einstein, physics, relativity, special, srt, transformation, velocity
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Difficulty
(2, default)
Points
2 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator uz
Decoration
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Link