Wiki-Quellcode von Lösung Pfahlbauten
Zuletzt geändert von Daniel Stocker am 2024/02/06 10:27
Verstecke letzte Bearbeiter
| author | version | line-number | content |
|---|---|---|---|
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6.1 | 1 | a) Bei den Pfosten befinden sich 3m oberhalb der Wasseroberfläche, da die x,,3,,-Koordinate des Punktes F gleich 3 ist. |
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2.1 | 2 | b) A(-2| 1|-4,5), B(5|1|-4,5),C(5|-5|-4,5), D(-2|-5|-4,5), E(-2|1|3), F(5|1|3), G(5|-5|3),H(-2|-5|3),I(1,5|1|5),J(1,5|-5|5) |
| 3 | c) {{formula}}\mid \overrightarrow{FG} \mid= \mid \overrightarrow{EH} \mid = 6{{/formula}} | ||
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4.1 | 4 | {{formula}}\mid \overrightarrow{FI} \mid = \mid \overrightarrow{OI}-\overrightarrow{OF} \mid = \left|\left(\begin{array}{c} 1,5-5 \\ 1-1 \\ 5-3\end{array}\right) \right|= \left| \left(\begin{array}{c} -3,5 \\ 0 \\ 2\end{array}\right) \right| = \sqrt{(-3,5)^2+0^2+2^2} = \frac{\sqrt{65}}{2} \approx 4,03{{/formula}} |
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5.1 | 5 | |
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7.1 | 6 | Dachfläche {{formula}} = 2 \cdot {{/formula}}Rechtecksfläche {{formula}}= 2 \cdot \frac{\sqrt{65}}{2} \cdot 6 FE = 6 \sqrt{65} FE \approx 48,37 FE{{/formula}} |
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11.1 | 7 | |
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7.2 | 8 | d) {{formula}}\overrightarrow{FI} = \left(\begin{array}{c} -3,5 \\ 0 \\ 2\end{array}\right){{/formula}} |
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11.1 | 9 | |
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7.2 | 10 | {{formula}}\overrightarrow{FE} = \left(\begin{array}{c} -2-5 \\ 1-1 \\ 3-3\end{array}\right)= \left(\begin{array}{c} -7 \\ 0 \\ 0\end{array}\right){{/formula}} |
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11.1 | 11 | |
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8.1 | 12 | {{formula}} cos(\alpha) = \frac{\overrightarrow{FI} \cdot \overrightarrow{FE}}{\mid \overrightarrow{FI} \mid \cdot \mid \overrightarrow{FE} \mid} = \frac{-3,5 \cdot -7 + 0 \cdot 0 + 2 \cdot 0}{ \frac{\sqrt{65}}{2} \cdot 7} = \frac{7}{\sqrt{65}}{{/formula}} |
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11.1 | 13 | |
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10.1 | 14 | {{formula}}\alpha \approx 29,74^{\circ}{{/formula}} |
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8.1 | 15 |