Kugelstoßen (2_070)

Grundkompetenz: AG 2.1, AG 4.1, FA 2.1, FA 4.3
Kugelstoßen ist eine Disziplin bei den Olympischen Sommerspielen.[br]Eine Metallkugel muss so weit wie möglich aus einem Kreis in einen vorgegebenen Aufschlagbereich gestoßen werden.[br]
a)
Im Jahr 1948 wurde bei den Männern ein neuer Weltrekord mit der Weite [math]17,68m[/math] aufgestellt. [br][br]Eine Faustregel besagt, dass sich seit 1948 der Weltrekord bei den Männern alle [math]2,5[/math] Jahre um [math]34cm[/math] verbessert hat. Die Weltrekordweite (in Metern) soll gemäß dieser Faustregel in Abhängigkeit von der Zeit [math]t[/math] (in Jahren) durch eine lineare Funktion [math]f[/math] beschrieben werden.[br][br][br][br][b][size=150]1) Erstellen Sie eine Gleichung der Funktion [math]f[/math]. Wählen Sie [math]t=0[/math] für das Jahr 1948.[/size][/b]
b)
Der Aufschlagbereich ist in der nachstehenden Abbildung in der Ansicht von oben dargestellt (alle Angaben in Metern). [br][img]data:image/png;base64,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[/img][br][br][br][br][b][size=150]1) Berechnen Sie den in der obigen Abbildung markierten Winkel [math]α[/math].[/size][/b]
c)
Die Bahnkurve einer gestoßenen Kugel lässt sich näherungsweise durch den Graphen der quadratischen Funktion [math]h[/math] beschreiben:[br][math]h\left(x\right)=-0,05x^2+0,75\cdot x+2[/math] mit [math]x\ge0[/math][br][math]x[/math]... horizontale Entfernung der Kugel von der Abstoßstelle in [math]m[/math][br][math]h\left(x\right)[/math]... Höhe der Kugel über dem Boden bei der horizontalen Entfernung [math]x[/math] in [math]m[/math][br][br][br][br][b][size=150]1) Ermitteln Sie, in welcher horizontalen Entfernung von der Abstoßstelle die Kugel auf dem Boden aufschlägt.[/size][/b]
d)
Für die bei den Männern verwendeten Kugeln gelten folgende Vorgaben:[br][list][*]Die Masse beträgt [math]7257g[/math].[/*][*]Der Durchmesser der Kugel liegt zwischen [math]11cm[/math] und [math]13cm[/math].[br][/*][/list]Eine Messing-Eisen-Legierung hat eine Dichte von [math]8,2g/cm^3[/math][sup][/sup].[br]Die Masse [math]m[/math] ist das Produkt aus Volumen [math]V[/math]und Dichte [math]\rho[/math], also [math]m=V\cdot\rho[/math].[br][br][br][br][b][size=150]1) Überprüfen Sie nachweislich, ob man aus dieser Messing-Eisen-Legierung eine Kugel herstellen kann, die diese Vorgaben erfüllt. [/size][/b]

Information: Kugelstoßen (2_070)