Zum Inhalt springen
Zuletzt geändert von Holger Engels am 2026/10/17 14:38
Von Version 47.1
bearbeitet von Holger Engels
am 2026/10/09 10:09
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 50.2
bearbeitet von Holger Engels
am 2026/10/09 11:24
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

Details

Seiteneigenschaften
Inhalt
... ... @@ -38,11 +38,11 @@
38 38  {{/aufgabe}}
39 39  
40 40  {{aufgabe id="Test-Rakete" afb="II" kompetenzen="K3,K4" quelle="Holger Engels" zeit="9"}}
41 -Bei der Erprobung eines neuen Raketenantriebs werden verschiedene Flugprofile getestet. Die Telemetrie wertet dabei aus, wie sich die Geschwindigkeit //v// (in m/s) über die Zeit //t// (in s) verändert (Geschwindigkeits-Zeit-Diagramm). Der orientierte Flächeninhalt unter dem Graphen der Geschwindigkeit entspricht dabei dem zurückgelegten Weg //s// (in m).
41 +Bei der Erprobung eines neuen Raketenantriebs werden verschiedene Flugprofile getestet. Bereits eingezeichnet in das Geschwindigkeits-Zeit-Diagramm ist ein unrealistisches Flugprofil, bei dem die Rakete schlagartig auf ihre Reisegeschwindigkeit kommt und diese die gesamten 20 Sekunden konstant hält.
42 42  
43 -Zeichne für jedes der folgenden Flugprofile einen möglichen Graphen der Geschwindigkeit //v(t)// in das Koordinatensystem ein. Allen drei Flugprofilen ist die Dauer von 20 Sekunden und die Strecke von 600 Metern gemein.
43 +[[image:Rakete.svg||width=600]]
44 +Zeichne für die beiden folgenden Flugprofile jeweils einen möglichen Graphen der Geschwindigkeit //v(t)// in das Koordinatensystem ein. Allen drei Flugprofilen ist die Dauer von 20 Sekunden und die Strecke von 600 Metern gemein.
44 44  (%class=abc%)
45 -1. Konstante Geschwindigkeit: Die Rakete legt in den ersten 20 Sekunden eine Strecke von genau 600 Metern zurück. Zur Vereinfachung gehen wir in diesem (unrealistischen) Testfall davon aus, dass die Rakete schlagartig auf ihre Reisegeschwindigkeit kommt und diese die gesamten 20 Sekunden konstant hält.
46 46  1. Konstante Beschleunigung: Die Rakete startet aus dem Stand (//v(0) = 0//) und beschleunigt für 20 Sekunden mit einer konstanten Rate. Die Geschwindigkeit nimmt also linear zu.
47 47  1. Start-, Flug- und Bremsphase: In einem weiteren Testflug startet die Rakete aus dem Stand (//v(0) = 0//), beschleunigt 8 Sekunden lang mit einer konstanten Rate, fliegt dann 4 Sekunden lang mit konstanter Geschwindigkeit und bremst schließlich mit einer konstanten negativen Rate wieder 8 Sekunden lang bis zum Stillstand (//v(20)=0//) ab.
48 48  {{/aufgabe}}
Rakete.ggb
Author
... ... @@ -1,0 +1,1 @@
1 +xwiki:XWiki.holgerengels
Größe
... ... @@ -1,0 +1,1 @@
1 +43.0 KB
Inhalt
Rakete.svg
Author
... ... @@ -1,0 +1,1 @@
1 +xwiki:XWiki.holgerengels
Größe
... ... @@ -1,0 +1,1 @@
1 +12.0 KB
Inhalt
... ... @@ -1,0 +1,1 @@
1 +<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="790" height="405"><defs><clipPath id="oizSQcIJNmlK"><path fill="none" stroke="none" d=" M 0 0 L 790 0 L 790 405 L 0 405 L 0 0 Z"/></clipPath></defs><g transform="scale(1,1)" clip-path="url(#oizSQcIJNmlK)"><g transform="translate(1.962519936203769,-13.739914692429977)"><rect fill="rgb(255,255,255)" stroke="none" x="0" y="0" width="1196" height="639" fill-opacity="1"/><path fill="none" stroke="rgb(180,179,186)" paint-order="fill stroke markers" d=" M 129.5 0.5 L 129.5 366.5 M 195.5 0.5 L 195.5 366.5 M 260.5 0.5 L 260.5 366.5 M 326.5 0.5 L 326.5 366.5 M 392.5 0.5 L 392.5 366.5 M 457.5 0.5 L 457.5 366.5 M 523.5 0.5 L 523.5 366.5 M 589.5 0.5 L 589.5 366.5 M 654.5 0.5 L 654.5 366.5 M 720.5 0.5 L 720.5 366.5 M 786.5 0.5 L 786.5 366.5 M 852.5 0.5 L 852.5 366.5 M 917.5 0.5 L 917.5 366.5 M 983.5 0.5 L 983.5 366.5 M 1049.5 0.5 L 1049.5 366.5 M 1114.5 0.5 L 1114.5 366.5 M 1180.5 0.5 L 1180.5 366.5" stroke-opacity="1" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(180,179,186)" paint-order="fill stroke markers" d=" M 76.5 0.5 L 76.5 366.5 M 90.5 0.5 L 90.5 366.5 M 103.5 0.5 L 103.5 366.5 M 116.5 0.5 L 116.5 366.5 M 142.5 0.5 L 142.5 366.5 M 155.5 0.5 L 155.5 366.5 M 168.5 0.5 L 168.5 366.5 M 181.5 0.5 L 181.5 366.5 M 208.5 0.5 L 208.5 366.5 M 221.5 0.5 L 221.5 366.5 M 234.5 0.5 L 234.5 366.5 M 247.5 0.5 L 247.5 366.5 M 273.5 0.5 L 273.5 366.5 M 287.5 0.5 L 287.5 366.5 M 300.5 0.5 L 300.5 366.5 M 313.5 0.5 L 313.5 366.5 M 339.5 0.5 L 339.5 366.5 M 352.5 0.5 L 352.5 366.5 M 365.5 0.5 L 365.5 366.5 M 379.5 0.5 L 379.5 366.5 M 405.5 0.5 L 405.5 366.5 M 418.5 0.5 L 418.5 366.5 M 431.5 0.5 L 431.5 366.5 M 444.5 0.5 L 444.5 366.5 M 471.5 0.5 L 471.5 366.5 M 484.5 0.5 L 484.5 366.5 M 497.5 0.5 L 497.5 366.5 M 510.5 0.5 L 510.5 366.5 M 536.5 0.5 L 536.5 366.5 M 549.5 0.5 L 549.5 366.5 M 562.5 0.5 L 562.5 366.5 M 576.5 0.5 L 576.5 366.5 M 602.5 0.5 L 602.5 366.5 M 615.5 0.5 L 615.5 366.5 M 628.5 0.5 L 628.5 366.5 M 641.5 0.5 L 641.5 366.5 M 668.5 0.5 L 668.5 366.5 M 681.5 0.5 L 681.5 366.5 M 694.5 0.5 L 694.5 366.5 M 707.5 0.5 L 707.5 366.5 M 733.5 0.5 L 733.5 366.5 M 746.5 0.5 L 746.5 366.5 M 760.5 0.5 L 760.5 366.5 M 773.5 0.5 L 773.5 366.5 M 799.5 0.5 L 799.5 366.5 M 812.5 0.5 L 812.5 366.5 M 825.5 0.5 L 825.5 366.5 M 838.5 0.5 L 838.5 366.5 M 865.5 0.5 L 865.5 366.5 M 878.5 0.5 L 878.5 366.5 M 891.5 0.5 L 891.5 366.5 M 904.5 0.5 L 904.5 366.5 M 930.5 0.5 L 930.5 366.5 M 943.5 0.5 L 943.5 366.5 M 957.5 0.5 L 957.5 366.5 M 970.5 0.5 L 970.5 366.5 M 996.5 0.5 L 996.5 366.5 M 1009.5 0.5 L 1009.5 366.5 M 1022.5 0.5 L 1022.5 366.5 M 1035.5 0.5 L 1035.5 366.5 M 1062.5 0.5 L 1062.5 366.5 M 1075.5 0.5 L 1075.5 366.5 M 1088.5 0.5 L 1088.5 366.5 M 1101.5 0.5 L 1101.5 366.5 M 1127.5 0.5 L 1127.5 366.5 M 1141.5 0.5 L 1141.5 366.5 M 1154.5 0.5 L 1154.5 366.5 M 1167.5 0.5 L 1167.5 366.5 M 1193.5 0.5 L 1193.5 366.5" stroke-opacity="0.23529411764705882" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(180,179,186)" paint-order="fill stroke markers" d=" M 63.5 13.5 L 1196.5 13.5 M 63.5 13.5 L 1196.5 13.5 M 63.5 64.5 L 1196.5 64.5 M 63.5 114.5 L 1196.5 114.5 M 63.5 164.5 L 1196.5 164.5 M 63.5 215.5 L 1196.5 215.5 M 63.5 265.5 L 1196.5 265.5 M 63.5 316.5 L 1196.5 316.5" stroke-opacity="1" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(180,179,186)" paint-order="fill stroke markers" d=" M 63.5 3.5 L 1196.5 3.5 M 63.5 3.5 L 1196.5 3.5 M 63.5 23.5 L 1196.5 23.5 M 63.5 33.5 L 1196.5 33.5 M 63.5 43.5 L 1196.5 43.5 M 63.5 54.5 L 1196.5 54.5 M 63.5 74.5 L 1196.5 74.5 M 63.5 84.5 L 1196.5 84.5 M 63.5 94.5 L 1196.5 94.5 M 63.5 104.5 L 1196.5 104.5 M 63.5 124.5 L 1196.5 124.5 M 63.5 134.5 L 1196.5 134.5 M 63.5 144.5 L 1196.5 144.5 M 63.5 154.5 L 1196.5 154.5 M 63.5 174.5 L 1196.5 174.5 M 63.5 185.5 L 1196.5 185.5 M 63.5 195.5 L 1196.5 195.5 M 63.5 205.5 L 1196.5 205.5 M 63.5 225.5 L 1196.5 225.5 M 63.5 235.5 L 1196.5 235.5 M 63.5 245.5 L 1196.5 245.5 M 63.5 255.5 L 1196.5 255.5 M 63.5 275.5 L 1196.5 275.5 M 63.5 285.5 L 1196.5 285.5 M 63.5 295.5 L 1196.5 295.5 M 63.5 305.5 L 1196.5 305.5 M 63.5 326.5 L 1196.5 326.5 M 63.5 336.5 L 1196.5 336.5 M 63.5 346.5 L 1196.5 346.5 M 63.5 356.5 L 1196.5 356.5" stroke-opacity="0.23529411764705882" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 63.5 2.5 L 63.5 366.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 63.5 1.5 L 59.5 5.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 63.5 1.5 L 67.5 5.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 63.5 366.5 L 1194.5 366.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 1195.5 366.5 L 1191.5 362.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 1195.5 366.5 L 1191.5 370.5" stroke-opacity="1" stroke-miterlimit="10"/><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="127" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">2</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="193" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">4</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="258" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">6</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="324" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">8</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="387" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">10</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="452" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">12</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="518" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">14</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="584" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">16</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="649" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">18</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="715" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">20</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="781" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">22</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="847" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">24</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="912" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">26</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="978" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">28</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="1044" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">30</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="1109" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">32</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="1175" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">34</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="43" y="321" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">10</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="43" y="270" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">20</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="43" y="220" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">30</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="43" y="169" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">40</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="43" y="119" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">50</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="43" y="69" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">60</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="43" y="18" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">70</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="49" y="382" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">0</text><path fill="none" stroke="rgb(176,0,32)" paint-order="fill stroke markers" d=" M 63.727272727273 215.29113227078193 L 720.6251993620406 215.29113227078193" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="3.5"/></g></g></svg>