\u5927\u5909\u3060\u3068\u3044\u3046\u8a71\u3002\u6388\u696d\u3067\u8a71\u3057\u305f\u3093\u3060\u3051\u3069\uff0c\u300c\u967d\u95a2\u6570\u3067\u89e3\u3051\u308b\u306e\u306b\uff0c\u306a\u305c\uff08\u308f\u3056\u308f\u3056\uff09\u9670\u95a2\u6570\u5b9a\u7406\u3084\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u672a\u5b9a\u4e57\u6570\u6cd5\u3092\u4f7f\u3063\u3066\u89e3\u3053\u3046\u3068\u3059\u308b\u3093\u3067\u3059\u304b\uff1f\u300d\u307f\u305f\u3044\u306a\u8868\u60c5\u3092\u8fd4\u3055\u308c\u305f\u306e\u3067\u3002<\/p>\n
\u3044\u3084\u3044\u3084\uff0c\u300c\u967d\u95a2\u6570\u3092\u4f7f\u3063\u3066\u89e3\u3053\u3046\u3068\u3059\u308b\u3068\u5927\u5909\u3067\u9014\u65b9\u306b\u304f\u308c\u305d\u3046\u306a\u554f\u984c\u3082\uff0c\u9670\u95a2\u6570\u5b9a\u7406\u3084\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u672a\u5b9a\u4e57\u6570\u6cd5\u3092\u4f7f\u3048\u3070\u7c21\u5358\u306b\u89e3\u3051\u308b\u3093\u3067\u3059\u3088\uff01\u300d\u3068\u3044\u3046\u3053\u3068\u3092\u8a00\u3044\u305f\u3044\u3002<\/p>\n
\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3082\u53c2\u7167\uff1a<\/p>\n
<\/p>\n
\\begin{eqnarray}
\nx(t, \\theta) &=& v_0 \\cos\\theta\\cdot t \\\\
\ny(t, \\theta) &=& h + v_0 \\sin\\theta\\cdot t – \\frac{1}{2} g \\,t^2
\n\\end{eqnarray}<\/p>\n
\u6ede\u7a7a\u6642\u9593 $\\tau(\\theta)$ \u3068\u306f $t=0$ \u3067\u6295\u5c04\u3057\u3066\u304b\u3089 $y=0$ \u306b\u306a\u308b\u307e\u3067\u306e\u6642\u9593\u3067\u3042\u308b\u3002$y(\\tau, \\theta) = 0$ \u3092\u6e80\u305f\u3059\u967d\u95a2\u6570 $\\tau(\\theta)$ \u3092\u6c42\u3081\u308b\u3002<\/p>\n
\\begin{eqnarray}
\ny(\\tau, \\theta)\u00a0 &=& h + v_0 \\sin\\theta\\cdot \\tau – \\frac{1}{2} g\\,\\tau^2 = 0
\n\\end{eqnarray}<\/p>\n
$\\tau$ \u306b\u3064\u3044\u3066\u306e2\u6b21\u65b9\u7a0b\u5f0f\u3060\u304b\u3089\u89e3\u306e\u516c\u5f0f\u304b\u3089<\/p>\n
\\begin{eqnarray}
\n\\tau &=& \\frac{-v_0 \\sin\\theta \\pm \\sqrt{v_0^2 \\sin^2\\theta + 2 g h}}{-g}
\n\\end{eqnarray}<\/p>\n
$\\tau(\\theta) > 0$ \u3067\u3042\u308b\u304b\u3089<\/p>\n
$$\\tau(\\theta) = \\frac{v_0 \\sin\\theta+ \\sqrt{v_0^2 \\sin^2\\theta + 2 g h}}{g}$$<\/p>\n
$\\tau(\\theta)$ \u304c\u967d\u95a2\u6570\u3068\u3057\u3066\uff0c\u5909\u6570 $\\theta$ \u3067\u3042\u304b\u3089\u3055\u307e\u306b\u8868\u3055\u308c\u3066\u3044\u308b\u3002<\/p>\n
\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $\\ell(\\theta)$ \u3068\u306f\u6ede\u7a7a\u6642\u9593 $\\tau(\\theta)$ \u306e\u9593\u306b\u6c34\u5e73\u65b9\u5411 ($x$ \u65b9\u5411) \u306b\u9032\u3080\u8ddd\u96e2\u3067\u3042\u308a\uff0c<\/p>\n
\\begin{eqnarray}
\n\\ell(\\theta) &=& x(\\tau(\\theta), \\theta) \\\\
\n&=& \\frac{v_0}{g} \\cos\\theta\\cdot\\left(v_0 \\sin\\theta + \\sqrt{v_0^2 \\sin^2\\theta + 2 g h} \\right)
\n\\end{eqnarray}<\/p>\n
$h=0$ \u306e\u3068\u304d\u306f<\/p>\n
\\begin{eqnarray}
\n\\ell(\\theta)
\n&=& \\frac{v_0}{g} \\cos\\theta\\cdot 2 v_0 \\sin\\theta \\\\
\n&=&\\frac{v_0^2}{g} \\sin 2\\theta
\n\\end{eqnarray}<\/p>\n
$\\ell(\\theta)$ \u304c\u6700\u5927\u3068\u306a\u308b $\\theta$ \u306f\u898b\u308b\u304b\u3089\u306b\u660e\u3089\u304b\u3060\u304c\uff0c\u5ff5\u306e\u305f\u3081<\/p>\n
\\begin{eqnarray}
\n\\frac{d}{d\\theta}\\ell(\\theta) &=& 2 \\frac{v_0^2}{g} \\cos 2\\theta = 0 \\quad\\mbox{\u3088\u308a}\\\\
\n\\theta &=& \\frac{\\pi}{4}
\n\\end{eqnarray}<\/p>\n
$h \\neq 0$ \u306e\u5834\u5408\u306b\u3082\uff0c\u539f\u7406\u7684\u306b\u306f\u540c\u3058\u3067 $\\dfrac{d}{d\\theta}\\ell(\\theta) = 0$ \u3068\u306a\u308b $\\theta$ \u3092\u6c42\u3081\u308c\u3070\u3044\u3044\u306e\u3067\u3042\u308b\u304c\uff0c\u4ee5\u4e0b\u306e\u8a08\u7b97…<\/p>\n
$$\\frac{d}{d\\theta}\\ell(\\theta) = \\frac{v_0}{g}\\frac{d}{d\\theta}\\left\\{ \\cos\\theta\\cdot\\left(v_0 \\sin\\theta + \\sqrt{v_0^2 \\sin^2\\theta + 2 g h} \\right)\\right\\} = \\cdots$$<\/p>\n
\u3084\u308b\u6c17\u3042\u308a\u307e\u3059\u304b\uff1f\u5168\u7136\u5148\u304c\u898b\u3048\u306a\u3044\u3093\u3060\u3051\u3069…<\/p>\n
\u300c\u9ad8\u3055 h \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u5230\u9054\u8ddd\u96e2\u306f\u89d2\u5ea645\u00b0\u306e\u3068\u304d\u3067\u306f\u306a\u3044<\/a>\u300d\u306e\u30da\u30fc\u30b8\u3067\u306f\uff08\u5909\u6570\u3092\u7121\u6b21\u5143\u5316\u5f8c\uff09\u9811\u5f35\u3063\u3066\u89e3\u3044\u3066\u3044\u308b\u3051\u3069\uff0c\u4eca\u898b\u8fd4\u3057\u3066\u307f\u3066\u3082\uff0c\u3082\u3046\u4e00\u5ea6\u3084\u308c\u3068\u8a00\u308f\u308c\u305f\u3089\u3061\u3087\u3063\u3068\u3084\u308b\u6c17\u304c\u304a\u304d\u306a\u3044…<\/p>\n \u3053\u306e\u3088\u3046\u306a\u62d8\u675f\u6761\u4ef6 $y(\\tau(\\theta), \\theta) = 0$ \u304c\u3042\u308b\u5834\u5408\u306e\u95a2\u6570 $x(\\tau(\\theta), \\theta)$ \u306e\u6975\u5024\u3092\u6c42\u3081\u308b\u554f\u984c\u306f\uff0c$y(\\tau(\\theta), \\theta) = 0$ \u3092\u6e80\u305f\u3059\u967d\u95a2\u6570 $\\tau(\\theta)$ \u3092\u4f7f\u3046\u3088\u308a\u3082\uff0c$\\tau(\\theta)$ \u3092\u00a0 $y(\\tau(\\theta), \\theta) = 0$ \u3092\u6e80\u305f\u3059\u9670\u95a2\u6570\u306e\u307e\u307e\uff0c\u9670\u95a2\u6570\u5b9a\u7406\u3092\u4f7f\u3063\u305f\u308a\uff0c\u3042\u308b\u3044\u306f\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u672a\u5b9a\u4e57\u6570\u6cd5\u3092\u4f7f\u3063\u3066\uff0c\u3088\u308a\u30b7\u30b9\u30c6\u30de\u30c6\u30a3\u30c3\u30af\u306b\uff08\u3042\u308b\u610f\u5473\u6a5f\u68b0\u7684\u306b\uff09\u89e3\u3044\u305f\u65b9\u304c\u7d50\u69cb\u7c21\u5358\u3067\u3042\u308b\u3093\u3060\u3088\u3002<\/p>\n \u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3082\u53c2\u7167\uff1a<\/p>\n \u5927\u5909\u3060\u3068\u3044\u3046\u8a71\u3002\u6388\u696d\u3067\u8a71\u3057\u305f\u3093\u3060\u3051\u3069\uff0c\u300c\u967d\u95a2\u6570\u3067\u89e3\u3051\u308b\u306e\u306b\uff0c\u306a\u305c\uff08\u308f\u3056\u308f\u3056\uff09\u9670\u95a2\u6570\u5b9a\u7406\u3084\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u672a\u5b9a\u4e57\u6570\u6cd5\u3092\u4f7f\u3063\u3066\u89e3\u3053\u3046\u3068\u3059\u308b\u3093\u3067\u3059\u304b\uff1f\u300d\u307f\u305f\u3044\u306a\u8868\u60c5\u3092\u8fd4\u3055\u308c\u305f\u306e\u3067\u3002<\/p>\n \u3044\u3084\u3044\u3084\uff0c\u300c\u967d\u95a2\u6570\u3092\u4f7f\u3063\u3066\u89e3\u3053\u3046\u3068\u3059\u308b\u3068\u5927\u5909\u3067\u9014\u65b9\u306b\u304f\u308c\u305d\u3046\u306a\u554f\u984c\u3082\uff0c\u9670\u95a2\u6570\u5b9a\u7406\u3084\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u672a\u5b9a\u4e57\u6570\u6cd5\u3092\u4f7f\u3048\u3070\u7c21\u5358\u306b\u89e3\u3051\u308b\u3093\u3067\u3059\u3088\uff01\u300d\u3068\u3044\u3046\u3053\u3068\u3092\u8a00\u3044\u305f\u3044\u3002<\/p>\n \u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3082\u53c2\u7167\uff1a<\/p>\n