(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 435152, 8172] NotebookOptionsPosition[ 430849, 8037] NotebookOutlinePosition[ 431292, 8056] CellTagsIndexPosition[ 431249, 8053] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Ujuja trajektoor k\[UDoubleDot]lghoovuse puhul, kui suunda hoitakse teatud \ punktile.\ \>", "Section", CellChangeTimes->{{3.6068290859105673`*^9, 3.6068291463220224`*^9}, { 3.6068411691535873`*^9, 3.606841170021637*^9}}], Cell[CellGroupData[{ Cell["\[CapitalUDoubleDot]lesande P\[UDoubleDot]stitus", "Subsubsection", CellChangeTimes->{{3.606829027759241*^9, 3.60682903299454*^9}}], Cell[TextData[{ "Ujuja ujub \[UDoubleDot]le j\[OTilde]e laiusega ", StyleBox["s", FontSlant->"Italic"], ", ta ujumise kiirus on ", StyleBox["vu", FontSlant->"Italic"], ", j\[OTilde]e voolu kiirus on ", StyleBox["vj", FontSlant->"Italic"], ". Ujuja v\[ADoubleDot]ljub punktist ", StyleBox["A", FontSlant->"Italic"], " ja suundub otse selle punkti vastas olevasse punkti ", StyleBox["B", FontSlant->"Italic"], ", mis asub punktist ", StyleBox["A", FontSlant->"Italic"], " samuti kaugusel ", StyleBox["s", FontSlant->"Italic"], ". Ujuja suundub kogu aeg punkti ", StyleBox["B ", FontSlant->"Italic"], "suunas. Leida ujuja trajektoori v\[OTilde]rrand, tema poolt \ l\[ADoubleDot]bitud tee pikkus ja trajektoori m\[ODoubleDot]\[ODoubleDot]da \ ujumiseks kulunud aeg." }], "Text", CellChangeTimes->{{3.6068287061208444`*^9, 3.6068290191937513`*^9}}, FontSize->10], Cell[BoxData[ RowBox[{ RowBox[{"Remove", "[", "\"\\"", "]"}], RowBox[{"(*", RowBox[{ RowBox[{ "See", " ", "on", " ", "k\[OTilde]ige", " ", "olulisem", " ", "k\[ADoubleDot]sk"}], ",", " ", RowBox[{ "mis", " ", "puhastab", " ", "programmi", " ", "m\[ADoubleDot]lu"}]}], "*)"}]}]], "Input", CellChangeTimes->{{3.6067642480581417`*^9, 3.6067642704331417`*^9}, { 3.6068286502466483`*^9, 3.606828676026123*^9}}], Cell[TextData[{ "Selleks, et liikumise v\[OTilde]rrandid tuleksid v\[OTilde]imalikult \ lihtsad, olgu l\[ADoubleDot]htepunkti A \nkoordinaadid (", StyleBox["s", FontSlant->"Italic"], "; 0) ja ujuja liikugu punkti ", StyleBox["B", FontSlant->"Italic"], "(0; 0) suunas. Siis on suunavektor \nsuunatud alati koordinaatide \ alguspunkti poole ja me saame seda esitada \nv\[OTilde]imalikult lihtsal \ kujul. J\[OTilde]gi voolaku ", StyleBox["y", FontSlant->"Italic"], "-teljega paralleelses suunas. Suvalisel ajahetkel \nolgu ", StyleBox["x", FontSlant->"Italic"], " olgu ujuja asukoha ", StyleBox["x", FontSlant->"Italic"], "-koordinaat ja ", StyleBox["y", FontSlant->"Italic"], " olgu ujuja asukoha ", StyleBox["y", FontSlant->"Italic"], "-koordinaat. \n\nNeed asukoha koordinaadid ja s\[OTilde]ltuvad ajast ", StyleBox["t", FontSlant->"Italic"], " ja kahest kiirusest - j\[OTilde]e voolu \nkiirusest ", StyleBox["vj", FontSlant->"Italic"], " ning ujuja kiirusest paigalseisvas vees ", StyleBox["vu", FontSlant->"Italic"], ". M\[OTilde]lemad kiirused on vektorid, \nmis on pikkuselt konstantsed. J\ \[OTilde]e voolu kiiruse vektori suund on alati sama mis ", StyleBox["y", FontSlant->"Italic"], "-teljel, \nujuja kiirusevektor on alati suunatud koordinaatide alguspunkti \ poole ja moodustab\n", StyleBox["x", FontSlant->"Italic"], "-teljega vastupidise suunaga alati nurga \[Alpha]. Liikumise alghetkel on \ see nurk 0\[Degree], \naga olenevalt j\[OTilde]e voolu kiiruse ja ujuja \ kiiruse suhtest v\[OTilde]ib see nurk suureneda \nkuni 90\[Degree]-ni.\n\n\ \[CapitalUDoubleDot]lesande \[UDoubleDot]heks tulemuseks v\[OTilde]iks olla \ ilmselt vektorv\[ADoubleDot]li, milles igale ujuja v\[OTilde]imalikule \n\ asukohapunktile vastab ujuja kiirusevektor. Samas, \[UDoubleDot]ritaks \ \[UDoubleDot]lesande lahendamisel v\[ADoubleDot]ltida \n\ v\[ADoubleDot]ljateooriat ja diferentsiaalv\[OTilde]rrandeid. \nEsimeseks \ eesm\[ADoubleDot]rgiks on leida ujuja v\[OTilde]imalike trajektooride v\ \[OTilde]rrandid v\[OTilde]imalikult lihtsal kujul.\n\n", StyleBox["\[CapitalUDoubleDot]lesannet saab k\[UDoubleDot]ll ilmselt \ suhteliselt lihtsalt lahendada diferentsv\[OTilde]rrandite abil, \naga siis \ on kursi \[UDoubleDot]mberarvutused igast konkreetsest ujuja ja j\[OTilde]e \ kiiruse \nv\[ADoubleDot]\[ADoubleDot]rtusest l\[ADoubleDot]htuvad (korraga \ saame k\[ADoubleDot]tte ainult \[UDoubleDot]he trajektoori!) ning \ trajektooriks \noleva murdjoone kuju hakkab veidi s\[OTilde]ltuma ka \ arvutussammu pikkuse (n\[ADoubleDot]iteks \niga sekundi tagant, v\[OTilde]i \ hoopis iga 2 sekundi tagant) valikust. 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