Exercise:
Ein Raumschiff des ADHS Alien Defence and Hit Squad funkt zur Basisstation der Erde dass sich dieser ein feindliches Alien-Raumschiff nähern würde; man sei ihm aber mit .c auf den Fersen und habe es bald eingeholt. Auf der Erde misst man für das angreife Alien-Raumschiff % der Lichtgeschwindigkeit. Wie schnell ist das ADHS-Raumschiff im Bezugssystem der Erde gemessen?

Solution:
Erste Möglichkeit: center tikzpicturescale. scope%Earth filldrawcolorblue fillblue!!white circle cm; drawred-latex --; drawred-latex --; nodered at .. mathcalS; scope scopescale. xscal xshift-cm yshiftcm %flaps coordinate P at --; drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scoperotate around:Pshift-cm-cmyscalexscal drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scope %rocket drawfillblack!!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; drawblulatex ---; drawblulatex --; nodeblue at - mathcalS'; drawcolorred thick stealth - -- nodeleft v; scope scopescale. xscal xshift-cm yshift-cm %flaps coordinate P at --; drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scoperotate around:Pshift-cm-cmyscalexscal drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scope %rocket drawfillyellow!!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; drawcolorred thickstealth- -- nodeleft u-.; drawcolorblue thickstealth- ---- noderight u'.c; scope tikzpicture center v fracu-u'-fracu'uc^ frac-.c-.c-frac-.c .cc^ -.c Zweite Möglichkeit: center tikzpicturescale. scope%Earth filldrawcolorblue fillblue!!white circle cm; drawred-latex --; drawred-latex --; nodered at .. mathcalS; scope scopescale. xscal xshift-cm yshiftcm %flaps coordinate P at --; drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scoperotate around:Pshift-cm-cmyscalexscal drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scope %rocket drawfillblack!!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; drawcolorred thick stealth - -- nodeleft u; drawcolorblue thickstealth- ---- nodeleft u'-.c; scope scopescale. xscal xshift-cm yshift-cm %flaps coordinate P at --; drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scoperotate around:Pshift-cm-cmyscalexscal drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scope %rocket drawfillyellow!!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; drawblulatex ---; drawblulatex --; nodeblue at - mathcalS'; drawcolorred thickstealth- -- nodeleft v-.; scope tikzpicture center u fracu'+v+fracu'vc^ frac-.c+-.c+frac-.c-.cc^ -.c