{"id":64541,"date":"2024-06-07T11:50:09","date_gmt":"2024-06-07T11:50:09","guid":{"rendered":"https:\/\/science-hub.click\/%E5%AE%89%E5%85%A8%E3%81%AE%E3%81%9F%E3%81%A8%E3%81%88%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-06-07T11:50:09","modified_gmt":"2024-06-07T11:50:09","slug":"%E5%AE%89%E5%85%A8%E3%81%AE%E3%81%9F%E3%81%A8%E3%81%88%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=64541","title":{"rendered":"\u5b89\u5168\u306e\u305f\u3068\u3048\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"

\u771f\u7a7a\u4e2d\u3001\u4e00\u69d8\u306a\u91cd\u529bg<\/strong>\u306e\u5834\u306b\u843d\u4e0b\u3059\u308b\u30dc\u30fc\u30eb B (\u521d\u901f\u5ea6 Vo \u3067\u767a\u5c04\u3055\u308c\u308b) \u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>

\u305d\u306e\u8ecc\u9053\u306f\u5782\u76f4\u9762 (O, Vo<\/strong> , g<\/strong> ) \u5185\u306b\u306a\u308a\u307e\u3059\u3002\u30ac\u30ea\u30ec\u30aa<\/a><\/span>(1568-1642) \u304c 1602 \u5e74\u306b\u8ff0\u3079\u305f\u6709\u540d\u306a\u81ea\u7531\u843d\u4e0b\u306e\u6cd5\u5247\u306b\u3088\u308b\u3068\u3001\u305d\u306e\u904b\u52d5\u306f\u305d\u306e\u8cea\u91cf<\/a><\/span>\u306b\u3082\u5bc6\u5ea6<\/a><\/span>\u306b\u3082\u4f9d\u5b58\u3057\u307e\u305b\u3093\u3002<\/p>

\u3053\u308c\u306f\u6b21\u306e 1 \u3064\u306e\u65b9\u7a0b\u5f0f\u306b\u3088\u3063\u3066\u6c7a\u307e\u308a\u307e\u3059\u3002 <\/p>

$$ {\\vec{OB} = \\frac {1}{2}.\\vec{g}.t^2+\\vec{V_0}.t} $$<\/div> \u3001<\/p>

\u3053\u308c\u306f\u3001(\u57fa\u5e95\u30d9\u30af\u30c8\u30ebg<\/strong>\u3068V\u00b0<\/strong>\u306e) \u30a2\u30d5\u30a3\u30f3\u5ea7\u6a19\u306b\u304a\u3051\u308b\u653e\u7269\u7dda<\/a><\/span>\u306e\u65b9\u7a0b\u5f0f<\/a><\/span>\u3067\u3059\u3002<\/p>

\u7279\u5b9a\u306e\u30e2\u30b8\u30e5\u30fc\u30eb V\u00b0 \u3067\u306f<\/strong>\u3001\u9283\u306e\u300c\u4e0a\u6607\u300d\u306b\u4e0e\u3048\u3089\u308c\u305f<\/span>\u65b9\u5411\u304c\u4f55\u3067\u3042\u308c\u3001\u7279\u5b9a\u306e\u70b9\u304c\u9283\u306e\u7bc4\u56f2\u5916\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u70b9\u306f\u3059\u3079\u3066\u3001<\/a><\/span>\u70b9<\/a><\/span>O \u3092\u300c\u56f2\u3080\u300d\u66f2\u7dda<\/a><\/span>(C) \u306b\u3088\u3063\u3066\u5236\u9650\u3055\u308c\u308b\u5e73\u9762\u306e\u9818\u57df\u3092\u5f62\u6210\u3057\u307e\u3059\u3002 (C) \u3092\u8d8a\u3048\u308b\u3068\u3001\u300c\u79c1\u305f\u3061\u306f\u5b89\u5168\u3067\u3059\u300d\u3068\u3044\u3046\u3053\u3068\u3067\u3001\u3053\u306e\u66f2\u7dda\u306e\u540d\u524d\u304c\u4ed8\u3051\u3089\u308c\u307e\u3057\u305f\u3002<\/p>

\u3053\u306e\u5834\u5408\u3001(C) \u306f\u653e\u7269\u7dda\u3067\u3042\u308b\u305f\u3081\u3001\u30bf\u30a4\u30c8\u30eb\u306f\u300c\u5b89\u5168\u653e\u7269\u7dda\u300d<\/a><\/span><\/strong>\u3067\u3059\u3002<\/p>

\u653e\u7269\u7dda\u306e\u9802\u70b9 H \u304b\u3089\u59cb\u307e\u308b\u6975\u5ea7\u6a19<\/a><\/span>\u3067\u306f\u3001\u305d\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {OP = r = \\frac {p}{(1 + cos \\theta)}} $$<\/div> \u3001 \u3068
$$ {p = \\frac{V_0^2}{g}} $$<\/div> (\u6c34\u5e73\u30b9\u30b3\u30fc\u30d7)\u3002<\/p>

\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3<\/a><\/span><\/span><\/h2>

\u305d\u308c\u306f\u30ac\u30ea\u30ec\u30aa\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u3001\u5f7c\u306e\u5f1f\u5b50\u3067\u3042\u308b\u30c8\u30ea\u30c1\u30a7\u30c3\u30ea\u306b\u3088\u3063\u3066\u6539\u826f\u3055\u308c\u307e\u3057\u305f (1640 \u5e74\u304b\u3089 1642 \u5e74\u307e\u3067)\u3002\u3053\u3053\u306b\u3042\u308a\u307e\u3059\uff1a<\/p>

\u03c6<\/span> =\u89d2\u5ea6<\/a><\/span>(OH,V\u00b0) \u3068\u3057\u307e\u3059\u3002 (C) \u4e0a\u306e\u6700\u5927\u7bc4\u56f2\u306e\u70b9\u3092 P \u3068\u3057\u307e\u3059\u3002 \u03b8 = 2\u03c6<\/span>\u3067\u3001OP = p\/2 c<\/i> o<\/i> s<\/i> 2<\/sup> \u03c6 (<\/span> p\/2 = OH) \u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>

OR<\/strong> = V\u00b0<\/strong> t \u3068\u3059\u308b\u3068\u3001\u4f55\u3082\u306a\u3044\u3088\u3046\u306a\u52d5\u304d\u306b\u306a\u308a\u307e\u3059\u3002 RP<\/strong> = -1\/2 g<\/strong> t^2\u5782\u76f4<\/a><\/span>\u964d\u4e0b\u3002<\/p>

\u7b49\u3057\u3044\u8fba OP=RP=RQ=OQ = 1\/2 gt^2\u3001\u4e2d\u5fc3 C \u3092\u6301\u3064\u3072\u3057\u5f62<\/a><\/span>OPRQ \u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u5bf8\u6cd5z<\/i> C \u306f<\/i><\/sub><\/span>OH \u306b\u5024\u3057\u307e\u3059\u3002\u6b21\u306b\u3001\u6b21\u306e\u3088\u3046\u306b\u8aad\u307f\u307e\u3059\u3002<\/p>

\u5e7e\u4f55\u5b66\u7684\u306b\u3001

$$ {OC = \\frac {OH}{cos\\phi}} $$<\/div>\u305d\u3057\u3066
$$ {OP = \\frac {OC}{cos\\phi}} $$<\/div><\/p>

\u3069\u3061\u3089\u304b

$$ {OP = \\frac {OH}{cos^2 \\phi}} $$<\/div> \u3001QED\u3002<\/p>
\n\"\u5b89\u5168\u306e\u305f\u3068\u3048\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u6b74\u53f2\u30e1\u30e2<\/span><\/h2>

\u30df\u30cb\u30de\u30e0\u30fb\u30e1\u30eb\u30bb\u30f3\u30cc\u795e\u7236\uff081588-1648\uff09\u306f\u3001\u3053\u306e\u3088\u3046\u306a\u5358\u7d14\u306a\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u306b\u9a5a\u304d\u3001\u5f53\u6642\u9752\u5e74\u3060\u3063\u305f\u30db\u30a4\u30d8\u30f3\u30b9\u9752\u5e74\uff081629-1695\uff09\u306b\u624b\u7d19\u3092\u9001\u308a\u3001\u30db\u30a4\u30d8\u30f3\u30b9\u306f\u3059\u3050\u306b\u300c\u305d\u306e\u901a\u308a\u3060\u300d\u3068\u8fd4\u4e8b\u3092\u304f\u308c\u305f\u3002<\/i><\/p>

\u3053\u308c\u3089\u306f\u7406\u8ad6\u7684\u306a<\/strong>\u554f\u984c\u3067\u3042\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u30dc\u30fc\u30eb\u306e\u5b9f\u969b\u306e\u8ecc\u9053<\/a><\/span>\u306b\u3064\u3044\u3066\u5fc3\u914d\u3059\u308b\u5fc5\u8981\u306f\u307e\u3063\u305f\u304f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>

\u5b9f\u969b\u306e\u3068\u3053\u308d\u3001\u30c8\u30ea\u30c1\u30a7\u30ea\u306f\u30ac\u30ea\u30ec\u30aa\u76f8\u5bfe\u6027\u7406\u8ad6\u3092\u521d\u3081\u3066\u5b9f\u8df5\u3057\u305f\u4eba\u3067\u3059\u3002\u5f7c\u306e\u30a2\u30a4\u30c7\u30a2\u306f?\u975e\u5e38\u306b\u5358\u7d14<\/strong>\u3067\u3059\u304c\u3001\u898b\u4e8b\u3067\u3059\u3002\u30dc\u30fc\u30eb B \u306e\u4f4d\u7f6e B1 \u304c\u4f55\u3067\u3042\u308c\u3001\u77ac\u9593<\/a><\/span>t1\u3001\u901f\u5ea6<\/a><\/span>V1 \u3067\u3001 \u5782\u76f4<\/a><\/span><\/strong>\u843d\u4e0bB1B<\/strong> = 1\/2 g<\/strong> ( t -t1)^2\u3002\u305d\u308c\u306f\u9593\u9055\u3044\u306a\u304f\u3001\u300c\u30e9\u30c1\u30a7\u30c3\u30c8\u30b1\u30fc\u30d6\u30eb\u30ab\u30fc\u300d\u306e\u6709\u540d\u306a\u30c7\u30b6\u30a4\u30f3\u3092\u521d\u3081\u3066\u63a1\u7528\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u3002\u30e2\u30d3\u30fc\u30eb\u306f\u63a5\u7dda\u65b9\u5411\u306e\u30b3\u30fc\u30b9<\/span>\u3092\u7d9a\u3051\u3001\u305d\u306e\u8ecc\u9053\u306b\u6cbf\u3063\u3066\u5f8c\u9000\u3057\u307e\u3059\u3002\u30db\u30a4\u30d8\u30f3\u30b9\u306f\u5e7c\u3044\u9803\u306b\u5b66\u3093\u3060\u305f\u3081\u3001\u5186\u904b\u52d5\u306e\u5411\u5fc3\u52a0\u901f\u5ea6<\/a><\/span>\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306f\u5f7c\u306b\u3068\u3063\u3066\u4f55\u306e\u554f\u984c\u3082\u3042\u308a\u307e\u305b\u3093\u3067\u3057\u305f (\u305f\u3060\u3057\u3001\u30db\u30a4\u30d8\u30f3\u30b9\u306f\u5e38\u306b\u9060\u5fc3\u529b<\/a><\/span>\u306b\u3064\u3044\u3066\u8a71\u3059\u3053\u3068\u3092\u597d\u3093\u3067\u3044\u307e\u3057\u305f)\u3002\u53d6\u308b\u3079\u304d\u30b9\u30c6\u30c3\u30d7\u306f 1 \u3064\u3060\u3051\u3067\u3057\u305f\u3002\u305d\u308c\u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u3067\u3057\u305f\u3002<\/p>

\n\"\u5b89\u5168\u306e\u305f\u3068\u3048\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u30ac\u30ea\u30ec\u30aa\u76f8\u5bfe\u6027\u7406\u8ad6\uff1f<\/span><\/h2>

\u3057\u304b\u3057\u3001\u3055\u3089\u306b\u91cd\u8981\u306a\u306e\u306f<\/strong>\u3001\u30c8\u30ea\u30c1\u30a7\u30ea\u306f\u6b21\u306e\u30ac\u30ea\u30ec\u30aa\u5171\u5206\u6563<\/a><\/span>\u554f\u984c\u3001\u3064\u307e\u308a\u958b\u59cb\u6642\u306e\u901f\u5ea6\u30bc\u30ed\u3092\u6b63\u5f0f\u306b\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u305f\u306e\u304b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u76f4\u611f\u7684\u306b\u306f\u3001\u4f53\u306f\u5782\u76f4\u306b\u5012\u308c\u307e\u3059: OB<\/strong> = k<\/strong> f(t)\u3002\u3053\u3053\u3067\u3001\u6163\u6027<\/span>\u306e\u539f\u7406\u3068<\/strong>\u30ac\u30ea\u30ec\u30aa\u76f8\u5bfe\u6027\u7406\u8ad6\u306e\u539f\u7406\u3001\u304a\u3088\u3073<\/strong>\u6cd5\u5247\u306e\u6642\u9593\u7684\u304a\u3088\u3073\u5c40\u6240\u7684\u4e0d\u5909\u6027\u3092\u9069\u7528\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002t1 \u3068 t2 \u306e 2\u500d<\/a><\/span>\u306b\u3064\u3044\u3066\u306f\u3001\u6b21\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>

OB<\/strong> (t1+t2) = V\u00b0<\/strong> (t1+t2) + k<\/strong> f(t1+t2) = OB1<\/strong> + V1<\/strong> .t2 + k<\/strong> f(t2)\u3001 OB1<\/strong> = V\u00b0<\/strong> .t1 + k<\/strong> f(t1) \u304a\u3088\u3073V1<\/strong> = V\u00b0<\/strong> + k<\/strong> f ‘(t1)\u3002<\/p>

f(t1+t2) = f(t1) +f(t2) +f ‘(t1).t2 \u3068\u3057\u307e\u3059\u3002<\/p>

t1 \u3068 t2 \u306f\u53ef\u63db\u3067\u3042\u308b\u305f\u3081\u3001f'(t1).t2 = f'(t2).t1: \u3057\u305f\u304c\u3063\u3066\u3001f'(t)\/t=cste;\u901f\u5ea6\u306f\u5fc5\u7136\u7684\u306b<\/strong>\u6642\u9593\u306e\u7dda\u5f62\u95a2\u6570<\/a><\/span>\u3067\u3059: f'(t) = gt: \u4f4d\u7f6e\u306b\u3088\u3063\u3066\u4e0d\u5909\u306a\u5834<\/a><\/span>\u3001\u3064\u307e\u308a\u3001\u4efb\u610f\u306e\u521d\u671f\u70b9<\/a><\/span>\u3067\u901f\u5ea6\u30bc\u30ed\u3001\u540c\u3058\u904b\u52d5\u3092\u751f\u6210\u3059\u308b\u3068\u3001\u30ac\u30ea\u30ec\u30aa\u76f8\u5bfe\u6027\u7406\u8ad6\u306f\u6642\u9593\u7684\u7dda\u5f62\u6027\u3092\u8ab2\u3057\u307e\u3059\u3002\u901f\u5ea6\u306e\uff1aV(t) = gt\u3002<\/p>

\u500b\u4eba\u7684\u306b\u306f\u3001\u3053\u306e\u3088\u3046\u306a\u8ad6\u6587\u3092<\/a><\/span>\u6700\u521d\u306b\u66f8\u3044\u305f\u4eba\u304c\u8ab0\u306a\u306e\u304b\u3092\u898b\u3064\u3051\u3089\u308c\u305f\u3089\u5b09\u3057\u3044\u3067\u3059:\u6307\u540d\u624b\u914d<\/span>\u901a\u77e5<\/a><\/span>\u3002\u524d\u3082\u3063\u3066\u611f\u8b1d\u3057\u307e\u3059\u3002<\/p>

\n\"\u5b89\u5168\u306e\u305f\u3068\u3048\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

(1\u30013\u30015\u30017…)<\/span><\/h2>

\u6b8b\u308a\u306e\u90e8\u5206\u306f\u3088\u304f\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u30ac\u30ea\u30ec\u30aa\u306f\u3001\u901f\u5ea6\u7dda\u56f3\u3092<\/a><\/span>\u975e\u5e38\u306b\u5de7\u307f\u306b\u4f5c\u6210\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u6709\u540d\u306a\u53f0\u5f62\u306e\u6cd5\u5247\u3092\u767a\u898b\u3057\u307e\u3057\u305f\u3002B1B2 = (V1+V2)\/2 .(t2-t1)\u3001\u3064\u307e\u308a\u30010+1\u30011 +2\u3001\u306a\u3069\u306e\u3088\u3046\u306b\u8ddd\u96e2\u304c\u5897\u52a0\u3057\u307e\u3059\u3002 2+3\u30013+4\u3001…\u4eca\u65e5\u306f\u6642\u4ee3\u932f\u8aa4\u7684\u3067\u7121\u5473\u4e7e\u71e5\u306a z = 1\/2 gt^2 \u3068\u8a00\u3046\u3053\u3068\u3092\u597d\u307f\u307e\u3059\u3002\u306f\u3044 \uff01\u6642\u9593\u304c\u3042\u308a\u307e\u305b\u3093\u3002<\/p>

\u305d\u3057\u3066\u3001 Torricelli V(x) = s<\/i> q<\/i> r<\/i> t<\/i> (2 g<\/i> x<\/i> )<\/span>\u3092\u8ffd\u52a0\u3057\u307e\u3059\u3002\u307e\u305f\u306fV<\/i> 2 2<\/sup> \u2212 V<\/i> 1 2<\/sup> = 2 g<\/i> ( z<\/i> 1 \u2212 z<\/i> 2)<\/span><\/p>

V1^2 + 2g z1 = V^2 + 2g.z = cste = (\u4eca\u65e5\u306e\u79c1\u305f\u3061\u306b\u3068\u3063\u3066\u306f 2E\u00b0) \u3068\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u79c1\u304c\u500b\u4eba\u7684\u306b\u8aad\u3093\u3060\u3053\u3068\u306e\u306a\u3044\u63a8\u8ad6\u306b\u3088\u3063\u3066\u3001\u5f7c\u304c\u6c34<\/a><\/span>\u306e\u6d41\u308c\u306b\u9069\u7528\u3059\u308b\u30c8\u30ea\u30c1\u30a7\u30ea\u306e\u516c\u5f0f\u3067\u3059\u3002 V^2 >0 \u3068\u3057\u3066\u3001\u6700\u5927\u306e z \u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u30c8\u30ea\u30c1\u30a7\u30c3\u30ea\u304c\u30e1\u30eb\u30bb\u30f3\u30cc\u3092\u4ecb\u3057\u3066\u82e5\u3044\u30db\u30a4\u30d8\u30f3\u30b9\u306b\u4f1d\u3048\u308b\u306e\u306f\u3053\u306e\u30a2\u30a4\u30c7\u30a2\u3067\u3059\u3002\u306f\u3044\u3001\u3053\u308c\u304c\u79d1\u5b66\u306e\u9032\u307f\u65b9\u3067\u3059\u3002\u3082\u3057\u79c1\u304c\u3055\u3089\u306b\u9060\u304f\u3092\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u305f\u3068\u3057\u305f\u3089\u3001\u305d\u308c\u306f\u79c1\u304c\u5de8\u4eba\u306e\u80a9\u306b\u4e57\u3063\u3066\u3044\u305f\u304b\u3089\u3067\u3059…<\/i><\/p><\/div>

\n\"\u5b89\u5168\u306e\u305f\u3068\u3048\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. Parabola of safety \u2013 anglais<\/a><\/li>
  2. \u041f\u0430\u0440\u0430\u0431\u043e\u043b\u0430 \u0431\u0435\u0437\u043e\u043f\u0430\u0441\u043d\u043e\u0441\u0442\u0438 \u2013 russe<\/a><\/li>
  3. Parabool \u2013 afrikaans<\/a><\/li>
  4. \u1263\u120b \u2013 amharique<\/a><\/li>
  5. \u0642\u0637\u0639 \u0645\u0643\u0627\u0641\u0626 \u2013 arabe<\/a><\/li>
  6. Parabola \u2013 azerba\u00efdjanais<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u5b89\u5168\u306e\u305f\u3068\u3048\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n