Last modified by Akiyoshi Yamakawa on 2026/02/26 20:31
From version 10.1
edited by Akiyoshi Yamakawa
on 2026/02/25 19:32
To version 11.1
edited by Akiyoshi Yamakawa
on 2026/02/25 20:53
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17 17  \\[[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?h<2||alt="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="14" width="35"]] [[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?\frac{L}{v}||alt="http://www.dietpanda.com/cgi-bin/mimetex.cgi?h<2\sqrt{gh}(\frac{L}{v}-4\sqrt{hg})-\frac{1}{2}g(\frac{L}{v}-4\sqrt{hg})^2" height="31" width="20"]] [[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?\sqrt{gh}-8h-\frac{1}{2}g\frac{L^2}{v^2}-8h+4||alt="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="42" width="250"]][[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?\frac{L}{v}||alt="http://www.dietpanda.com/cgi-bin/mimetex.cgi?h<2\sqrt{gh}(\frac{L}{v}-4\sqrt{hg})-\frac{1}{2}g(\frac{L}{v}-4\sqrt{hg})^2" height="31" width="20"]][[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?\sqrt{gh}||alt="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="21" width="40"]]
18 18  \\[[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?0<6\sqrt{gh}||alt="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="24" width="90"]][[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?\frac{L}{v}||alt="http://www.dietpanda.com/cgi-bin/mimetex.cgi?h<2\sqrt{gh}(\frac{L}{v}-4\sqrt{hg})-\frac{1}{2}g(\frac{L}{v}-4\sqrt{hg})^2" height="31" width="20"]][[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?-17h-\frac{1}{2}g\frac{L^2}{v^2}||alt="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="42" width="130"]]** これを、ｖの二次不等式に直すと、**
19 19  \\[[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、**
20 -\\[[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="65" width="474"]] 　**ｖの下限なので、－の方をとって、**
20 +\\[[image:http://www.dietpanda.com/cgi-bin/mimetex.cgi?v={\frac{6\sqrt{\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="65" width="474"]] 　**ｖの下限なので、－の方をとって、**
21 21  \\[[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="55" width="747"]]　　**・・・答え**
22 22  \\**注：次元解析して速度の単位になっていることも確認！　(% style="font-size: 18px; font-family: Georgia, serif" %)√(% style="font-size:18px;" %){(m/s^^2^^)/m)}m=m/s(%%)**