Changes for page 2025-Ryudai-Butsuri-Q2A(3)
Last modified by Akiyoshi Yamakawa on 2026/02/21 18:40
From version 5.1
edited by Akiyoshi Yamakawa
on 2026/02/19 19:11
on 2026/02/19 19:11
To version 6.1
edited by Akiyoshi Yamakawa
on 2026/02/19 19:14
on 2026/02/19 19:14
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... ... @@ -16,6 +16,6 @@ 16 16 \\[[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?h<2\frac{L}{v}\sqrt{gh}-8h-\frac{1}{2}g\frac{L^2}{v^2}-8h+4\frac{L}{v}\sqrt{gh}||height="40" width="345"]] 17 17 \\[[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?0<6\sqrt{gh}\frac{L}{v}-17h-\frac{1}{2}g\frac{L^2}{v^2}||height="43" width="250"]] **これを、ｖの二次不等式に直すと、** 18 18 \\[[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?0>34v^2-12\sqrt{\frac{g}{h}}Lv+\frac{g}{h}L^2||alt="http://www.dietpanda.com/cgi-bin/mimetex.cgi?0>34v^2-12\sqrt{gh}v+\frac{g}{h}" height="40" width="200"]] **さらに、＝０の二次方程式としてvを求めると、** 19 -\\[[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?v=\frac{6\frac{g}{h}L\pm\sqrt{36\frac{g}{h}L-34\frac{g}{h}L}}{34}=\frac{(6\pm\sqrt{2})\sqrt{\frac{g}{h}}L}{34}||alt="http://www.dietpanda.com/cgi-bin/mimetex.cgi?v=\frac{6\frac{g}{h}\pm\sqrt{36\frac{g}{h}-34\frac{g}{h}}}{34}=\frac{(6\pm\sqrt{2})\sqrt{\frac{g}{h}}}{34}" height="46" width="320"]] **ｖの下限なので、－の方をとって、** 19 +\\[[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?v=\frac{6\frac{g}{h}L\pm\sqrt{36\frac{g}{h}L^2-34\frac{g}{h}L^2}}{34}=\frac{(6\pm\sqrt{2})\sqrt{\frac{g}{h}}L}{34}||alt="http://www.dietpanda.com/cgi-bin/mimetex.cgi?v=\frac{6\frac{g}{h}\pm\sqrt{36\frac{g}{h}-34\frac{g}{h}}}{34}=\frac{(6\pm\sqrt{2})\sqrt{\frac{g}{h}}}{34}" height="46" width="320"]] **ｖの下限なので、－の方をとって、** 20 20 \\[[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?v=\frac{(6-sqrt{2})}{34}\sqrt{\frac{g}{h}}L=\frac{(6-sqrt{2})(6+sqrt{2})}{34(6+sqrt{2})}\sqrt{\frac{g}{h}}L=\frac{34}{34(6+\sqrt{2})}\sqrt{\frac{g}{h}}L=\frac{1}{(6+\sqrt{2})}\sqrt{\frac{g}{h}}L||alt="http://www.dietpanda.com/cgi-bin/mimetex.cgi?v=\frac{(6-sqrt{2})}{34}\sqrt{\frac{g}{h}}}=\frac{(6-sqrt{2})(6+sqrt{2})}{34(6+sqrt{2})}}\sqrt{\frac{g}{h}}=\frac{34}{34(6+\sqrt{2})}\sqrt{\frac{g}{h}}=\frac{1}{(6+\sqrt{2})}\sqrt{\frac{g}{h}}" height="50" width="500"]] **・・・答え** 21 21 \\**（注：次元解析して速度の単位になっていることも確認！ √{(m/s^^2^^)/m)}m=m/s）**