{"id":27246,"date":"2021-09-25T13:00:01","date_gmt":"2021-09-25T13:00:01","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27246"},"modified":"2024-09-16T11:50:56","modified_gmt":"2024-09-16T11:50:56","slug":"%e5%a6%82%e4%bd%95%e8%ae%a1%e7%ae%97%e6%8a%95%e5%b0%84%e8%bf%90%e5%8a%a8","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e5%a6%82%e4%bd%95%e8%ae%a1%e7%ae%97%e6%8a%95%e5%b0%84%e8%bf%90%e5%8a%a8\/","title":{"rendered":"\u6295\u5c04\u8fd0\u52a8"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u6295\u5c04\u8fd0\u52a8<\/h1>\n<p><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n\u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e\u6295\u5c04\u8fd0\u52a8\u7684\u6240\u6709\u8fd0\u52a8\u5b66\u65b9\u9762\uff0c\u8fd9\u662f\u7269\u7406\u5b66\u4e2d\u7684\u4e00\u4e2a\u5173\u952e\u4e3b\u9898\uff0c\u5b83\u6269\u5c55\u4e86\u6211\u4eec\u4e4b\u524d\u5bf9\u5300\u52a0\u901f\u8fd0\u52a8\u7684\u7814\u7a76\u3002\u6211\u4eec\u5c06\u8ba8\u8bba\u5982\u4f55\u5728\u53d6\u6d88\u5bf9\u8fd0\u52a8\u65b9\u5411\u7684\u9650\u5236\u540e\uff0c\u6211\u4eec\u4f1a\u9047\u5230\u5178\u578b\u7684\u6295\u5c04\u7269\u7684\u629b\u7269\u7ebf\u8f68\u8ff9\u3002\u6211\u4eec\u5c06\u7814\u7a76\u5982\u4f55\u5728\u4efb\u4f55\u65b9\u5411\u7684\u521d\u901f\u5ea6\u4e0e\u7531\u4e8e\u91cd\u529b\u4ea7\u751f\u7684\u52a0\u901f\u5ea6\u76f8\u7ed3\u5408\u7684\u60c5\u51b5\u4e0b\uff0c\u5f62\u6210\u8fd9\u4e9b\u8fd0\u52a8\u3002<br \/>\n.<\/em><\/p>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5728\u672c\u8282\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ol>\n<li><strong>\u56de\u5fc6<\/strong>\u6295\u5c04\u8fd0\u52a8\u7684\u57fa\u672c\u65b9\u7a0b\u548c\u4e0e\u6295\u5c04\u7269\u53d1\u5c04\u76f8\u5173\u7684\u5b9a\u4e49\uff08\u5982\u521d\u901f\u5ea6\u3001\u53d1\u5c04\u89d2\u3001\u91cd\u529b\u52a0\u901f\u5ea6\uff09\u3002<\/li>\n<li><strong>\u56fe\u5f62\u5316\u89e3\u91ca<\/strong>\u6295\u5c04\u7269\u7684\u8f68\u8ff9\u3002<\/li>\n<li><strong>\u89e3\u91ca<\/strong>\u8fd0\u52a8\u7684\u4e0d\u540c\u9636\u6bb5\uff08\u4e0a\u5347\u3001\u6700\u9ad8\u70b9\u3001\u4e0b\u964d\uff09\u5982\u4f55\u4e0e\u8fd0\u52a8\u5b66\u65b9\u7a0b\u76f8\u5173\u8054\u3002<\/li>\n<li><strong>\u89e3\u51b3<\/strong>\u6d89\u53ca\u4f7f\u7528\u629b\u7269\u7ebf\u8fd0\u52a8\u65b9\u7a0b\u8ba1\u7b97\u6295\u5c04\u7269\u7684\u6700\u5927\u9ad8\u5ea6\u3001\u6c34\u5e73\u8ddd\u79bb\u548c\u603b\u98de\u884c\u65f6\u95f4\u7684\u95ee\u9898\u3002<\/li>\n<li><strong>\u5206\u89e3<\/strong>\u6295\u5c04\u8fd0\u52a8\u7684\u65b9\u7a0b\uff0c\u4ee5\u7406\u89e3\u6bcf\u4e2a\u7ec4\u6210\u90e8\u5206\uff08\u521d\u901f\u5ea6\u3001\u53d1\u5c04\u89d2\u3001\u7531\u4e8e\u91cd\u529b\u4ea7\u751f\u7684\u52a0\u901f\u5ea6\uff09\u5982\u4f55\u5f71\u54cd\u603b\u8f68\u8ff9\u3002<\/li>\n<\/ol>\n<p><center><\/p>\n<p><strong>\u5185\u5bb9\u76ee\u5f55<\/strong><br \/>\n<a href=\"#1\"><strong>\u4ecb\u7ecd<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u6295\u5c04\u8fd0\u52a8\u7684\u53d1\u5c55<\/strong><\/a><br \/>\n<a href=\"#3\">\u5982\u4f55\u786e\u5b9a\u6295\u5c04\u7269\u8fbe\u5230\u7684\u6700\u5927\u9ad8\u5ea6\uff1f<\/a><br \/>\n<a href=\"#4\">\u5982\u4f55\u786e\u5b9a\u6295\u5c04\u8fd0\u52a8\u7684\u8303\u56f4\uff1f<\/a><br \/>\n<a href=\"#5\">\u4ec0\u4e48\u53d1\u5c04\u89d2\u5ea6\u80fd\u6700\u5927\u5316\u6295\u5c04\u7269\u7684\u8303\u56f4\uff1f<\/a><br \/>\n<a href=\"#6\"><strong>\u5efa\u8bae\u7ec3\u4e60<\/strong><\/a>\n<\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/_dXgQ_7u5GE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<\/div>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u4ecb\u7ecd<\/h2>\n<p style=\"text-align: justify; color: #000000;\">\u5728\u4e4b\u524d\u7684\u8bfe\u7a0b\u4e2d\uff0c\u6211\u4eec\u7814\u7a76\u4e86<a href=\"https:\/\/www.youtube.com\/watch?v=P21bsNFF9Fw\" rel=\"noopener\" target=\"_blank\">\u5300\u52a0\u901f\u76f4\u7ebf\u8fd0\u52a8<\/a>\uff0c\u5e76\u4e86\u89e3\u4e86\u5f53\u5300\u52a0\u901f\u65bd\u52a0\u5728\u4e0e\u8fd0\u52a8\u65b9\u5411\u76f8\u540c\u7684\u65b9\u5411\u65f6\u4f1a\u53d1\u751f\u4ec0\u4e48\u3002\u5f53\u6211\u4eec\u53d6\u6d88\u5bf9\u65b9\u5411\u7684\u9650\u5236\u65f6\uff0c\u6211\u4eec\u5f97\u5230\u7684\u662f\u5300\u52a0\u901f\u8fd0\u52a8\uff0c\u4f46\u4e0d\u518d\u662f\u76f4\u7ebf\u8fd0\u52a8\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u8fd0\u52a8\u6cbf\u7740\u629b\u7269\u7ebf\u7684\u4e00\u90e8\u5206\u8fdb\u884c\uff0c\u8fd9\u5c31\u662f\u6295\u5c04\u8fd0\u52a8\u7684\u7814\u7a76\u5f00\u59cb\u7684\u5730\u65b9\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5728\u6295\u5c04\u8fd0\u52a8\u4e2d\uff0c\u521d\u901f\u5ea6\u53ef\u4ee5\u5728\u4efb\u4f55\u65b9\u5411\u4e0a\u7ed9\u51fa\uff0c\u800c\u52a0\u901f\u5ea6\u5219\u9075\u5faa\u91cd\u529b\u7684\u5178\u578b\u65b9\u5411\u3002\u5f53\u6295\u5c04\u7269\u76f4\u63a5\u5411\u4e0a\u53d1\u5c04\u65f6\uff0c\u6211\u4eec\u5f97\u5230\u7684\u662f\u4e00\u4e2a\u5782\u76f4\u53d1\u5c04\uff0c\u8fd9\u662f\u4e00\u79cd\u5300\u52a0\u901f\u8fd0\u52a8\u7684\u60c5\u51b5\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u6295\u5c04\u8fd0\u52a8\u7684\u53d1\u5c55<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_dXgQ_7u5GE&amp;t=172s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u6295\u5c04\u7269<\/span><\/strong><\/a>\u4ece\u5730\u9762\u7531\u4e00\u95e8\u5927\u70ae\u4ee5\u521d\u901f\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">v_0<\/span> \u548c\u4e00\u4e2a\u503e\u89d2 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u5411\u7a7a\u4e2d\u53d1\u5c04\u3002\u8fd9\u4e2a\u6295\u5c04\u7269\u7684\u8fd0\u52a8\u53ef\u4ee5\u901a\u8fc7\u63d0\u53d6\u5176\u8f68\u8ff9\u65b9\u7a0b\u6765\u5efa\u6a21\uff0c\u8fd9\u4e9b\u65b9\u7a0b\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\vec{a}(t) &amp; = (0,-g) \\\\ \\\\\n\n\\vec{v}(t) &amp; =\\displaystyle \\int (0,-g) dt = (v_{0x}, -gt+v_{0y})\\\\ \\\\\n\n\\vec{r}(t) &amp; =\\displaystyle \\int (v_{0x}, -gt+v_{0y}) dt = \\left(v_{0x}t + x_0, -\\frac{1}{2}gt^2+v_{0y}t + y_0\\right)\n\n\\end{array}<\/span>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-JQFKmGORl8A\/YVB9tKzayMI\/AAAAAAAAFks\/KPaXIUIcIVQ2yOAa_N9leIPgcZY6iv5zQCLcBGAsYHQ\/s0\/proyectil.PNG\" width=\"694\" height=\"390\" alt=\"\u6295\u5c04\u7269\u7684\u53d1\u5c04\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-JQFKmGORl8A\/YVB9tKzayMI\/AAAAAAAAFks\/KPaXIUIcIVQ2yOAa_N9leIPgcZY6iv5zQCLcBGAsYHQ\/s0\/proyectil.PNG\" width=\"694\" height=\"390\" alt=\"\u6295\u5c04\u7269\u7684\u53d1\u5c04\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{v}_{0} = (v_{0x},v_{0y})<\/span> \u662f\u521d\u901f\u5ea6\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}_0=(x_0,y_0)<\/span> \u662f\u521d\u59cb\u4f4d\u7f6e\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">g=9.81[m\/s^2]<\/span> \u662f\u91cd\u529b\u52a0\u901f\u5ea6\u7684\u5927\u5c0f\u3002\u73b0\u5728\uff0c\u5982\u679c\u6211\u4eec\u89c2\u5bdf\u524d\u9762\u7684\u6bb5\u843d\uff0c\u6211\u4eec\u4f1a\u6ce8\u610f\u5230\u6ca1\u6709\u76f4\u63a5\u6307\u51fa\u6295\u5c04\u7269\u7684\u901f\u5ea6\uff0c\u800c\u662f\u5b83\u7684\u901f\u7387\u548c\u53d1\u5c04\u89d2\u3002\u4ece\u8fd9\u4e9b\u4fe1\u606f\u548c\u4e00\u70b9\u4e09\u89d2\u5b66\u53ef\u4ee5\u786e\u5b9a\u521d\u901f\u5ea6\uff0c\u56e0\u4e3a\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nv_{0x} &amp;= v_0 \\cos(\\theta) \\\\\n\nv_{0y} &amp;= v_0 \\sin(\\theta)\n\n\\end{array}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">v_0 = \\|\\vec{v}_0\\|<\/span> \u662f\u521d\u901f\u5ea6\u7684\u5927\u5c0f\u3002\u5982\u679c\u6211\u4eec\u518d\u52a0\u4e0a\u521d\u59cb\u4f4d\u7f6e <span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0)=(0,0)<\/span>\uff0c\u8f68\u8ff9\u65b9\u7a0b\u8868\u8fbe\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\vec{a}(t) &amp; = (0,-g) \\\\ \\\\\n\n\\vec{v}(t) &amp; =(v_{0}\\cos(\\theta), -gt+v_{0}\\sin(\\theta)\\\\ \\\\\n\n\\vec{r}(t) &amp; \\displaystyle =\\left(v_{0}\\cos(\\theta)t , -\\frac{1}{2}gt^2+v_{0}\\sin(\\theta)t \\right)\n\n\\end{array}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u6709\u4e86\u8fd9\u4e9b\u6211\u4eec\u5c31\u53ef\u4ee5\u56de\u7b54\u4e00\u4e9b\u4e0e\u6295\u5c04\u7269\u53d1\u5c04\u6709\u5173\u7684\u95ee\u9898\uff1a\u5b83\u80fd\u8d70\u591a\u8fdc\uff1f\u5b83\u80fd\u8fbe\u5230\u4ec0\u4e48\u9ad8\u5ea6\uff1f\u5b83\u9700\u8981\u591a\u957f\u65f6\u95f4\u624d\u80fd\u6389\u4e0b\u6765\uff1f\u7b49\u7b49\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u5982\u4f55\u786e\u5b9a\u6295\u5c04\u7269\u8fbe\u5230\u7684\u6700\u5927\u9ad8\u5ea6\uff1f<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_dXgQ_7u5GE&amp;t=398s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u8981\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898<\/span><\/strong><\/a>\u6211\u4eec\u5fc5\u987b\u95ee\u81ea\u5df1\uff1a\u5f53\u6295\u5c04\u7269\u8fbe\u5230\u5176\u6700\u5927\u9ad8\u5ea6\u65f6\u4f1a\u53d1\u751f\u4ec0\u4e48\uff1f\u53d1\u751f\u7684\u4e8b\u60c5\u662f\u5b83\u7684\u5782\u76f4\u901f\u5ea6\u5206\u91cf\u53d8\u4e3a\u96f6\uff0c\u56e0\u6b64\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\"> -gt+v_{0}\\sin(\\theta) = 0 <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u76f8\u5f53\u4e8e\u8bf4\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\"> t = \\displaystyle \\frac{v_{0}\\sin(\\theta)}{g} <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u4e5f\u5c31\u662f\u8bf4\uff0c\u6295\u5c04\u7269\u5728\u53d1\u5c04\u540e\u7ecf\u8fc7 <span class=\"katex-eq\" data-katex-display=\"false\">t=v_0\\sin(\\theta)\/g<\/span> \u7684\u65f6\u95f4\u8fbe\u5230\u6700\u5927\u9ad8\u5ea6\u3002\u6211\u4eec\u79f0\u4e4b\u4e3a\u00bb\u6700\u5927\u9ad8\u5ea6\u65f6\u95f4\u00bb\uff0c\u5e76\u5199\u4f5c\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{t_{alt.max} = \\frac{v_{0}\\sin(\\theta)}{g}}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u7136\u540e\uff0c\u6295\u5c04\u7269\u80fd\u591f\u8fbe\u5230\u7684\u6700\u5927\u9ad8\u5ea6\u53ef\u4ee5\u901a\u8fc7\u5728\u6295\u5c04\u7269\u4f4d\u7f6e\u7684\u5782\u76f4\u5206\u91cf\u4e2d\u66ff\u6362 <span class=\"katex-eq\" data-katex-display=\"false\">t=t_{alt.max}<\/span> \u6765\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\ny_{alt.max} &amp; = \\displaystyle -\\frac{1}{2}gt_{alt.max}^2+v_{0}\\sin(\\theta)t_{alt.max}\\\\ \\\\\n\n&amp; =\\displaystyle-\\frac{1}{2}g \\left(\\frac{v_{0}\\sin(\\theta)}{g} \\right)^2 + v_{0}\\sin(\\theta) \\frac{v_{0}\\sin(\\theta)}{g} \\\\ \\\\\n\n&amp; =\\displaystyle-\\frac{1}{2} \\frac{v_{0}^2\\sin^2(\\theta)}{g} + \\frac{v_{0}^2\\sin^2(\\theta)}{g} \\\\ \\\\\n\n&amp; =\\displaystyle \\frac{v_{0}^2\\sin^2(\\theta)}{2g}\n\n\\end{array}<\/span>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u5982\u4f55\u786e\u5b9a\u6295\u5c04\u8fd0\u52a8\u7684\u8303\u56f4\uff1f<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_dXgQ_7u5GE&amp;t=653s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5982\u679c\u4f60\u60f3\u77e5\u9053<\/span><\/strong><\/a>\u6295\u5c04\u7269\u5728\u89e6\u5730\u4e4b\u524d\u8d70\u4e86\u591a\u8fdc\uff0c\u4f60\u53ea\u9700\u8981\u5411\u4e0e\u6295\u5c04\u7269\u53d1\u5c04\u76f8\u5173\u7684\u8f68\u8ff9\u65b9\u7a0b\u8be2\u95ee\u3002\u4f46\u6211\u4eec\u5982\u4f55\u505a\u5230\u8fd9\u4e00\u70b9\u5462\uff1f\u7b80\u5355\uff1a\u5f53\u6295\u5c04\u7269\u89e6\u5730\u65f6\u4f1a\u53d1\u751f\u4ec0\u4e48\uff1f\u53d1\u751f\u7684\u4e8b\u60c5\u662f\u4e0e\u9ad8\u5ea6\u76f8\u5173\u7684\u4f4d\u7f6e\u5750\u6807\u53d8\u4e3a\u96f6\uff0c\u5373\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle -\\frac{1}{2}gt^2+v_{0}\\sin(\\theta)t = 0\n\n<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u5728\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u89e3\u51fa\u6295\u5c04\u7269\u89e6\u5730\u7684\u65f6\u95f4\uff0c\u8fd9\u53d1\u751f\u5728\u4e24\u4e2a\u65f6\u523b\uff1a\u53d1\u5c04\u65f6\u523b\u548c\u5b83\u843d\u5730\u65f6\u523b\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u65b9\u7a0b\u7684\u53ef\u80fd\u89e3\u662f\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nt &amp; = 0\\\\ \\\\\n\nt &amp; = \\displaystyle \\frac{2v_0 \\sin(\\theta)}{g}\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u6211\u4eec\u79f0\u975e\u96f6\u89e3\u4e3a\u00bb\u4e0b\u964d\u65f6\u95f4\u00bb\uff0c\u5e76\u5199\u4f5c\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{t_{caida} = \\displaystyle \\frac{2v_0 \\sin(\\theta)}{g}}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c\u4f60\u56de\u987e\u4e0a\u6587\uff0c\u4f60\u4f1a\u53d1\u73b0 <span class=\"katex-eq\" data-katex-display=\"false\">t_{caida} = 2t_{alt.max}<\/span> \u56e0\u4e3a\u6295\u5c04\u7269\u8fbe\u5230\u6700\u5927\u9ad8\u5ea6\u6240\u9700\u7684\u65f6\u95f4\u4e0e\u4ece\u6700\u9ad8\u70b9\u4e0b\u964d\u6240\u9700\u7684\u65f6\u95f4\u76f8\u540c\u3002\u8fd9\u8868\u660e\u4e86\u6295\u5c04\u8fd0\u52a8\u4e2d\u7684\u67d0\u79cd\u5bf9\u79f0\u6027\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5f53\u4f60\u6ce8\u610f\u5230\u4e0e\u9ad8\u5ea6\u76f8\u5173\u7684\u5750\u6807\u5177\u6709\u629b\u7269\u7ebf\u7684\u5f62\u72b6\u65f6\uff0c\u8fd9\u79cd\u5bf9\u79f0\u6027\u5df2\u7ecf\u663e\u73b0\u51fa\u6765\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u77e5\u9053\u4e0b\u964d\u65f6\u95f4\u540e\uff0c\u73b0\u5728\u53ef\u4ee5\u901a\u8fc7\u5728\u7b2c\u4e00\u4e2a\u4f4d\u7f6e\u5750\u6807\u4e2d\u66ff\u6362\u5b83\u6765\u8ba1\u7b97\u6295\u5c04\u7269\u89e6\u5730\u65f6\u8d70\u4e86\u591a\u8fdc\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nx_{caida} &amp;= v_{0}\\cos(\\theta)t_{caida} \\\\ \\\\\n\n&amp; = \\displaystyle v_{0}\\cos(\\theta)\\frac{2v_0 \\sin(\\theta)}{g} \\\\ \\\\\n\n&amp; = \\displaystyle \\frac{v_0^2 \\sin(2\\theta)}{g} \\\\ \\\\\n\n\\end{array}<\/span>\n<p><a name=\"5\"><\/a><\/p>\n<h3>\u4ec0\u4e48\u53d1\u5c04\u89d2\u5ea6\u80fd\u6700\u5927\u5316\u6295\u5c04\u7269\u7684\u8303\u56f4\uff1f<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_dXgQ_7u5GE&amp;t=999s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5982\u679c\u4f60\u60f3\u77e5\u9053<\/span><\/strong><\/a>\u4ec0\u4e48\u53d1\u5c04\u89d2\u5ea6\u80fd\u6700\u5927\u5316\u6295\u5c04\u7269\u7684\u8303\u56f4\uff0c\u6216\u8005\u4f60\u60f3\u8bc1\u660e\u4f60\u6240\u77e5\u9053\u7684\u662f\u786e\u5b9e\u6b63\u786e\u7684\uff0c\u4f60\u53ea\u9700\u8981\u4ece\u6211\u4eec\u5df2\u7ecf\u8bc1\u660e\u7684\u8868\u8fbe\u5f0f\u4e2d\u53d6\u51fa\u4e00\u4e2a\uff0c\u5141\u8bb8\u4f60\u4ee5\u6570\u5b66\u65b9\u5f0f\u63d0\u51fa\u95ee\u9898\u3002\u6211\u4eec\u5df2\u7ecf\u5728\u524d\u4e00\u90e8\u5206\u4e2d\u8ba1\u7b97\u4e86\u4e0b\u964d\u8ddd\u79bb\uff0c\u5e76\u4e14\u5b83\u662f\u53d1\u5c04\u89d2\u7684\u4e00\u4e2a\u51fd\u6570\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle x_{caida} = x_{caida}(\\theta) = \\frac{v_0^2 \\sin(2\\theta)}{g}\n\n<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u6b63\u5f26\u51fd\u6570\u6709\u4e24\u4e2a\u53ef\u80fd\u7684\u6781\u503c\uff1a+1 \u548c -1\uff0c\u4f46\u6211\u4eec\u53ea\u5bf9\u524d\u8005\u611f\u5174\u8da3\u3002\u8981\u4f7f <span class=\"katex-eq\" data-katex-display=\"false\">\\sin(2\\theta)=+1<\/span>\uff0c\u9700\u8981 <span class=\"katex-eq\" data-katex-display=\"false\">2\\theta = 90^o<\/span>\uff08+ <span class=\"katex-eq\" data-katex-display=\"false\">2k\\pi,<\/span> \u4f46\u6211\u4eec\u7701\u7565\u8fd9\u4e00\u90e8\u5206\u56e0\u4e3a\u4e0d\u9700\u8981\uff09\uff0c\u56e0\u6b64 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta=45^o<\/span> \u662f\u4f7f\u8303\u56f4\u6700\u5927\u7684\u53d1\u5c04\u89d2\u3002\u8fd9\u4e2a\u95ee\u9898\u4e5f\u53ef\u4ee5\u901a\u8fc7\u5c06\u5176\u4f5c\u4e3a\u4f18\u5316\u95ee\u9898\uff08\u4f7f\u7528<a href=\"https:\/\/www.youtube.com\/watch?v=OscTlX3raaE&#038;list=PL_C8rbeFjqAVaR_sgLJRBvMm5t6E1GxGI\" target=\"_blank\" rel=\"noopener\">\u8fd9\u95e8\u5fae\u79ef\u5206\u8bfe\u7684\u5de5\u5177<\/a>\uff09\u6765\u89e3\u51b3\uff0c\u4f46\u6211\u9009\u62e9\u4e86\u8fd9\u6761\u66f4\u5feb\u4e14\u540c\u6837\u5177\u6709\u8bf4\u660e\u6027\u7684\u8def\u5f84\u3002<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u5efa\u8bae\u7ec3\u4e60<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\u4e00\u4e2a\u6295\u5c04\u7269\u4ece\u5730\u9762\u4ee5 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta=30^o<\/span> \u7684\u4ef0\u89d2\u548c <span class=\"katex-eq\" data-katex-display=\"false\">v_0=70[km\/h].<\/span> \u7684\u521d\u901f\u5ea6\u53d1\u5c04\u3002a) \u6295\u5c04\u7269\u8fbe\u5230\u7684\u6700\u5927\u9ad8\u5ea6\u662f\u591a\u5c11\uff1f b) \u6295\u5c04\u7269\u5728\u89e6\u5730\u524d\u8d70\u4e86\u591a\u8fdc\uff1f c) \u6295\u5c04\u7269\u9700\u8981\u591a\u957f\u65f6\u95f4\u624d\u80fd\u843d\u5730\uff1f<\/li>\n<li>\u4e00\u95e8\u653e\u5728\u5730\u9762\u7684\u70ae\u4ee5 90[km\/h] \u7684\u901f\u5ea6\u53d1\u5c04\u4e00\u9897\u5b50\u5f39\u3002\u5e94\u5c06\u70ae\u8c03\u6574\u5230\u4ec0\u4e48\u4ef0\u89d2\uff0c\u4f7f\u5b50\u5f39\u5728\u6c34\u5e73\u8ddd\u79bb 20[m] \u7684\u5730\u65b9\u843d\u4e0b\uff1f<\/li>\n<li>\u524d\u4e00\u4e2a\u7ec3\u4e60\u4e2d\u7684\u76f8\u540c\u70ae\u73b0\u5728\u88ab\u653e\u7f6e\u5728 5[m] \u7684\u9ad8\u5ea6\u3002\u5e94\u5c06\u70ae\u8c03\u6574\u5230\u4ec0\u4e48\u4ef0\u89d2\uff0c\u4f7f\u5b50\u5f39\u4ecd\u7136\u5728\u6c34\u5e73\u8ddd\u79bb 20[m] \u7684\u5730\u65b9\u843d\u4e0b\uff1f<\/li>\n<li>\u4e00\u67b6\u8f70\u70b8\u673a\u5728\u79bb\u5730\u9762 3,000[m] \u7684\u9ad8\u5ea6\u4ee5 1,500[km\/h] \u7684\u901f\u5ea6\u98de\u884c\u3002\u5982\u679c\u5b83\u56e0\u81ea\u91cd\u800c\u6295\u4e0b\u4e00\u4e2a\u6295\u5c04\u7269\uff0c\u8be5\u6295\u5c04\u7269\u4ece\u6295\u4e0b\u5230\u89e6\u5730\u95f4\u8d70\u4e86\u591a\u8fdc\uff1f<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u6295\u5c04\u8fd0\u52a8 \u6458\u8981\uff1a \u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e\u6295\u5c04\u8fd0\u52a8\u7684\u6240\u6709\u8fd0\u52a8\u5b66\u65b9\u9762\uff0c\u8fd9\u662f\u7269\u7406\u5b66\u4e2d\u7684\u4e00\u4e2a\u5173\u952e\u4e3b\u9898\uff0c\u5b83\u6269\u5c55\u4e86\u6211\u4eec\u4e4b\u524d\u5bf9\u5300\u52a0\u901f\u8fd0\u52a8\u7684\u7814\u7a76\u3002\u6211\u4eec\u5c06\u8ba8\u8bba\u5982\u4f55\u5728\u53d6\u6d88\u5bf9\u8fd0\u52a8\u65b9\u5411\u7684\u9650\u5236\u540e\uff0c\u6211\u4eec\u4f1a\u9047\u5230\u5178\u578b\u7684\u6295\u5c04\u7269\u7684\u629b\u7269\u7ebf\u8f68\u8ff9\u3002\u6211\u4eec\u5c06\u7814\u7a76\u5982\u4f55\u5728\u4efb\u4f55\u65b9\u5411\u7684\u521d\u901f\u5ea6\u4e0e\u7531\u4e8e\u91cd\u529b\u4ea7\u751f\u7684\u52a0\u901f\u5ea6\u76f8\u7ed3\u5408\u7684\u60c5\u51b5\u4e0b\uff0c\u5f62\u6210\u8fd9\u4e9b\u8fd0\u52a8\u3002 . \u5b66\u4e60\u76ee\u6807\uff1a \u5728\u672c\u8282\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u56de\u5fc6\u6295\u5c04\u8fd0\u52a8\u7684\u57fa\u672c\u65b9\u7a0b\u548c\u4e0e\u6295\u5c04\u7269\u53d1\u5c04\u76f8\u5173\u7684\u5b9a\u4e49\uff08\u5982\u521d\u901f\u5ea6\u3001\u53d1\u5c04\u89d2\u3001\u91cd\u529b\u52a0\u901f\u5ea6\uff09\u3002 \u56fe\u5f62\u5316\u89e3\u91ca\u6295\u5c04\u7269\u7684\u8f68\u8ff9\u3002 \u89e3\u91ca\u8fd0\u52a8\u7684\u4e0d\u540c\u9636\u6bb5\uff08\u4e0a\u5347\u3001\u6700\u9ad8\u70b9\u3001\u4e0b\u964d\uff09\u5982\u4f55\u4e0e\u8fd0\u52a8\u5b66\u65b9\u7a0b\u76f8\u5173\u8054\u3002 \u89e3\u51b3\u6d89\u53ca\u4f7f\u7528\u629b\u7269\u7ebf\u8fd0\u52a8\u65b9\u7a0b\u8ba1\u7b97\u6295\u5c04\u7269\u7684\u6700\u5927\u9ad8\u5ea6\u3001\u6c34\u5e73\u8ddd\u79bb\u548c\u603b\u98de\u884c\u65f6\u95f4\u7684\u95ee\u9898\u3002 \u5206\u89e3\u6295\u5c04\u8fd0\u52a8\u7684\u65b9\u7a0b\uff0c\u4ee5\u7406\u89e3\u6bcf\u4e2a\u7ec4\u6210\u90e8\u5206\uff08\u521d\u901f\u5ea6\u3001\u53d1\u5c04\u89d2\u3001\u7531\u4e8e\u91cd\u529b\u4ea7\u751f\u7684\u52a0\u901f\u5ea6\uff09\u5982\u4f55\u5f71\u54cd\u603b\u8f68\u8ff9\u3002 \u5185\u5bb9\u76ee\u5f55 \u4ecb\u7ecd \u6295\u5c04\u8fd0\u52a8\u7684\u53d1\u5c55 \u5982\u4f55\u786e\u5b9a\u6295\u5c04\u7269\u8fbe\u5230\u7684\u6700\u5927\u9ad8\u5ea6\uff1f \u5982\u4f55\u786e\u5b9a\u6295\u5c04\u8fd0\u52a8\u7684\u8303\u56f4\uff1f \u4ec0\u4e48\u53d1\u5c04\u89d2\u5ea6\u80fd\u6700\u5927\u5316\u6295\u5c04\u7269\u7684\u8303\u56f4\uff1f \u5efa\u8bae\u7ec3\u4e60 \u4ecb\u7ecd 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