Last modified by Akiyoshi Yamakawa on 2026/02/26 20:36
From version 11.1
edited by Akiyoshi Yamakawa
on 2026/02/21 22:15
To version 12.1
edited by Akiyoshi Yamakawa
on 2026/02/26 20:36
Change comment: There is no comment for this version

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... ... @@ -9,8 +9,8 @@
9 9  \\(% style="font-size: 20px; font-family: Georgia, serif" %)**//(//**(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)**//1/2//**(% style="font-size: 20px; font-family: Georgia, serif" %)**//)g//**(% style="font-family: Georgia, serif; font-size: 22px" %)**//t//**(% style="font-size: 20px; font-family: Georgia, serif" %)**//,,0,,^^2^^=8h//**(% style="font-size:20px;" %)**　より　**(% style="font-family: Georgia, serif; font-size: 22px" %)**//t//**(% style="font-family: Georgia, serif; font-size: 20px" %)**//,,0,, = 4√(h/g)//**(%%)
10 10  (% style="font-size:18px;" %)** **(%%)
11 11  (% style="font-family: Georgia, serif; font-size: 22px" %)**//vt//**(% style="font-family: Georgia, serif; font-size: 20px" %)**// = L//**(% style="font-size:20px;" %)** より、**(% style="font-family: Georgia, serif; font-size: 22px" %)**//t//**(% style="font-family: Georgia, serif; font-size: 20px" %)**// //= //L/v//**(%%)
12 -(% style="font-size:18px;" %)** **(%%)**
13 -(% style="font-family: Georgia, serif; font-size: 20px" %)//(//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//1/2//(% style="font-family: Georgia, serif; font-size: 20px" %)//)m//(% style="font-family: Georgia, serif; font-size: 22px" %)//v//(% style="font-size: 20px; font-family: Georgia, serif" %)//,,y,,^^2^^=mh (8h)//(% style="font-size:20px;" %)// //より、(% style="font-size: 20px; font-family: Georgia, serif" %)//u=(//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//1/2//(% style="font-size: 20px; font-family: Georgia, serif" %)//)//(% style="font-family: Georgia, serif; font-size: 22px" %)//v//(% style="font-family: Georgia, serif; font-size: 20px" %)//,,y,,=//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//2//(% style="font-family: Georgia, serif; font-size: 20px" %)//√//(% style="font-size: 20px; font-family: Georgia, serif" %)//(gh)//(%%)**
12 +(% style="font-size:18px;" %)** **(%%)
13 +(% style="font-family: Georgia, serif; font-size: 20px" %)**//(//**(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)**//1/2//**(% style="font-family: Georgia, serif; font-size: 20px" %)**//)m//**(% style="font-family: Georgia, serif; font-size: 22px" %)**//v//**(% style="font-size: 20px; font-family: Georgia, serif" %)**//,,y,,^^2^^=mh (8h)//**(% style="font-size:20px;" %)**// //より、**(% style="font-size: 20px; font-family: Georgia, serif" %)**//u=(//**(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)**//1/2//**(% style="font-size: 20px; font-family: Georgia, serif" %)**//)//**(% style="font-family: Georgia, serif; font-size: 22px" %)**//v//**(% style="font-family: Georgia, serif; font-size: 20px" %)**//,,y,,=//**(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)**//2//**(% style="font-family: Georgia, serif; font-size: 20px" %)**//√//**(% style="font-size: 20px; font-family: Georgia, serif" %)**//(gh)//**(%%)
14 14  
15 15  * **時刻ｔでの高さｙが障害物の高さｈよりも上であればよいので、
16 16  \\(% style="font-family: Georgia, serif; font-size: 22px" %)//h < y=u (t - t,,0,,) - (//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 22px" %)//1/2//(% style="font-family: Georgia, serif; font-size: 22px" %)//)g(t - t,,0,,)^^2^^//(%%)**
... ... @@ -22,7 +22,7 @@
22 22  (% style="font-size: 20px; font-family: Georgia, serif; font-size: 22px" %)//　//(%%)
23 23  (% style="font-family: Georgia, serif; font-size: 22px" %)//０>//(% style="font-size:22px;" %)//34//(% style="font-family: Georgia, serif; font-size: 22px" %)//v^^2^^ - //(% style="font-size:22px;" %)//12//(% style="font-family: Georgia, serif; font-size: 22px" %)//L√(g/h)v //(% style="font-family: Georgia, serif; font-size: 20px" %)//+ //(% style="font-size: 20px; font-family: Georgia, serif; font-size: 22px" %)//(g/h)L^^2^^ //(%%)さらに、＝０の二次方程式としてvを求めると、
24 24  　
25 -(% style="font-size: 20px; font-family: Georgia, serif" %)//v=[//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//6//(% style="font-size: 20px; font-family: Georgia, serif" %)//(g/h)±√{//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//36//(% style="font-size: 20px; font-family: Georgia, serif" %)//(g/h)L^^2^^ - //(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//34//(% style="font-size: 20px; font-family: Georgia, serif" %)//(g/h)L^^2^^}]///(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//34//(% style="font-size: 20px; font-family: Georgia, serif" %)// =[(//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//6//(% style="font-size: 20px; font-family: Georgia, serif" %)//±√//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//2//(% style="font-size: 20px; font-family: Georgia, serif" %)//)L√(g/h)]///(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//34//(% style="font-size: 20px; font-family: Georgia, serif" %)// //(%%)ｖの下限なので、－の方をとって、
25 +(% style="font-size: 20px; font-family: Georgia, serif" %)//v=[//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//6//(% style="font-size: 20px; font-family: Georgia, serif" %)//√(g/h)±√{//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//36//(% style="font-size: 20px; font-family: Georgia, serif" %)//(g/h)L^^2^^ - //(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//34//(% style="font-size: 20px; font-family: Georgia, serif" %)//(g/h)L^^2^^}]///(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//34//(% style="font-size: 20px; font-family: Georgia, serif" %)// =[(//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//6//(% style="font-size: 20px; font-family: Georgia, serif" %)//±√//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//2//(% style="font-size: 20px; font-family: Georgia, serif" %)//)L√(g/h)]///(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//34//(% style="font-size: 20px; font-family: Georgia, serif" %)// //(%%)ｖの下限なので、－の方をとって、
26 26  \\(% style="font-size: 20px; font-family: Georgia, serif" %)//v=[(//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//6 - //(% style="font-size: 20px; font-family: Georgia, serif" %)//√//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//2//(% style="font-size: 20px; font-family: Georgia, serif" %)//)L√(g/h)]///(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//34//(% style="font-size: 20px; font-family: Georgia, serif" %)// = [(//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//6 - //(% style="font-size: 20px; font-family: Georgia, serif" %)//√//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//2//(% style="font-size: 20px; font-family: Georgia, serif" %)//)(//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//6 + //(% style="font-size: 20px; font-family: Georgia, serif" %)//√//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//2//(% style="font-size: 20px; font-family: Georgia, serif" %)//)L√(g/h)]///(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//{34//(% style="font-size: 20px; font-family: Georgia, serif" %)//(//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//6 + //(% style="font-size: 20px; font-family: Georgia, serif" %)//√//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//2//(% style="font-size: 20px; font-family: Georgia, serif" %)//)}=[34L√(g/h)]///(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//{34//(% style="font-size: 20px; font-family: Georgia, serif" %)//(//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//6 + //(% style="font-size: 20px; font-family: Georgia, serif" %)//√//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//2//(% style="font-size: 20px; font-family: Georgia, serif" %)//)}
27 27  \\ =[L√(g/h)]/(//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//6 + //(% style="font-size: 20px; font-family: Georgia, serif" %)//√//(% style="font-family: Arial, Helvetica, sans-serif; font-size: 20px" %)//2//(% style="font-size: 20px; font-family: Georgia, serif" %)//)　//(% style="font-size: 16px; font-family: Arial, Helvetica, sans-serif" %)・・・答え(%%)**
28 28  **（注：次元解析して速度の単位になっていることも確認！　m(% style="font-family:Georgia,serif;" %)√(%%){(m/s^^2^^)/m}=m/s )**

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