Exercise:
Aliens haben auf der Erde Dokumente gestohlen und flüchten nun in ihrem Raumschiff mit .c. Wie schnell müsste ein Jagd-Raumschiff des ADHS Alien Defence and Hit Squad von der Erde wegfliegen damit es sich dem Alien-UFO mit .c nähern würde?

Solution:
center tikzpicturescale. scope%Earth filldrawcolorblue fillblue!!white circle cm; drawred-latex --; drawred-latex --; nodered 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; drawblulatex --; drawblulatex --; nodeblue at mathcalS'; drawcolorred thick stealth - --. noderight v; scope scopescale. xshiftcm 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; drawcolorblue thickstealth- ---- nodeleft u'-.c; drawcolorred thickstealth- -- noderight u.c; scope tikzpicture center Aufgrund der Skizze und u fracu'+v+fracvu'c^ folg müsste die Geschwindigkeit v fracu-u'-fracuu'c^ fracu c - up c-fracu cup cc^ bet c v betragen.