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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
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Auf Version 51.2
bearbeitet von Holger Engels
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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 +Der Flächeninhalt unter dem Graphen der Geschwindigkeit entspricht dem zurückgelegten Weg //s// (in m).
45 +
46 +Zeichne für die beiden folgenden Flugprofile jeweils einen möglichen Graphen 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}}
49 49  
52 +{{aufgabe id="Streifenmethode" afb="II" kompetenzen="" quelle="Stefanie Walz" zeit=""}}
53 +[[Freier Fall.svg||width=300 class=right]]Das Schaubild zeigt die Höhe über der Zeit für einen Fall aus 5 Metern Höhe, modelliert durch die Funktion {{formula}}h(t)=-5\cdot t^2+5{{/formula}}. Für //n// Streifen und einer Streifenbreite von {{formula}}\fracbn{{/formula}} ergibt sich die Untersumme folgendermaßen:
54 +
55 +{{formula}}U_n = \Delta x \cdot h(1\Delta x) + \Delta x \cdot h(2\Delta x) + ... + \Delta x \cdot h(n\Delta x){{/formula}}
56 +{{formula}}U_n = \Delta x \cdot 5 \dot 1^2 + \Delta x \cdot 5 \dot 2^2 + ... + \Delta x \cdot 5 \dot n^2{{/formula}}
57 +{{formula}}U_n = -5\cdot b^3\frac16(2+\frac3n+\frac1n^2+5b{{/formula}}
58 +
59 +{{/aufgabe}}
60 +
50 50  == Bestimmtes Integral ==
51 51  
52 52  == Eigenschaften ==
Rakete.ggb
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Inhalt
Rakete.svg
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Größe
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