{"id":26622,"date":"2011-05-03T11:23:41","date_gmt":"2011-05-03T03:23:41","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=26622"},"modified":"2021-10-06T16:27:03","modified_gmt":"2021-10-06T08:27:03","slug":"%e5%b9%b3%e9%9d%a2%e7%ad%89%e5%8a%a0%e9%80%9f%e5%ba%a6%e9%81%8b%e5%8b%95%e8%a7%a3%e9%a1%8c%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"http:\/\/localhost\/%e5%b9%b3%e9%9d%a2%e7%ad%89%e5%8a%a0%e9%80%9f%e5%ba%a6%e9%81%8b%e5%8b%95%e8%a7%a3%e9%a1%8c%e6%96%b9%e6%b3%95\/","title":{"rendered":"\u5e73\u9762\u7b49\u52a0\u901f\u5ea6\u904b\u52d5\u89e3\u984c\u65b9\u6cd5"},"content":{"rendered":"

\u5e73\u9762\u7b49\u52a0\u901f\u5ea6\u904b\u52d5\u89e3\u984c\u65b9\u6cd5
\n<\/span>\u570b\u7acb\u82d1\u88e1\u9ad8\u7d1a\u4e2d\u5b78\u7269\u7406\u79d1\u8a31\u5bb6\u9298\u8001\u5e2b\/\u570b\u7acb\u5f70\u5316\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb\u6d2a\u9023\u8f1d\u6559\u6388\u8cac\u4efb\u7de8\u8f2f<\/span><\/strong><\/p>\n

\u4e00\u822c\u800c\u8a00\uff0c\u7576\u6211\u5011\u8655\u7406\u5e73\u9762\u7b49\u52a0\u901f\u5ea6\u904b\u52d5\u6642\uff0c\u6703\u5c07\u6240\u8655\u7406\u7684\u5ea7\u6a19\u5206\u70ba\u5169\u500b\u76f8\u4e92\u5782\u76f4\u7684\u65b9\u5411\uff0c\uff08\u5982\uff1a\u6c34\u5e73\u65b9\u5411\u8207\u925b\u76f4\u65b9\u5411\u3001\u5e73\u884c\u659c\u9762\u65b9\u5411\u8207\u5782\u76f4\u659c\u9762\u65b9\u5411\u3001\u5207\u7dda\u65b9\u5411\u8207\u6cd5\u7dda\u65b9\u5411\u2026\u7b49\uff09\u5728\u5404\u81ea\u7684\u65b9\u5411\u4e0a\u4ee5\u76f4\u7dda\u904b\u52d5\u7684\u6982\u5ff5\u89e3\u984c\uff0c\u5728\u4f9d\u5176\u9700\u8981\u5408\u4f75\u5373\u5f97\u89e3\uff0c\u4eca\u5929\u8003\u616e\u5e73\u9762\u5411\u91cf\u53ca\u6b63\u5f26\u5b9a\u7406\uff0c\u90e8\u5206\u984c\u578b\u53ef\u4ee5\u4e0d\u9808\u5206\u89e3\u5373\u53ef\u6c42\u89e3\uff0c\u901a\u7528\u4f8b\u984c\u5982\u4e0b\uff1a<\/p>\n

\u4f8b\u984c\uff1a
\n\u67d0\u7269\u9ad4\u81ea\u5730\u9762\uff08\u6216\u96e2\u5730\u9ad8 $$h$$\uff09\u4ee5\u521d\u901f\u5ea6 $$v_0$$\u00a0\u8207\u6c34\u5e73\u593e $$\\theta$$ \u89d2\u659c\u5411\u62cb\u51fa\uff0c\u5728\u51fa\u767c\u5f8c\u6642\u523b $$t$$ \u6642\uff0c\u7269\u9ad4\u7684\u901f\u5ea6\u70ba $$v$$ \u4e14\u8207\u6c34\u5e73\u65b9\u5411\u593e\u89d2 $$\\varphi$$\uff1a<\/p>\n

1.\u00a0 \u7269\u9ad4\u7684\u901f\u5ea6 $$v$$ \uff1a
\n<\/span><\/strong>\u7531\u52a0\u901f\u5ea6\u7684\u5b9a\u7fa9\uff1a<\/p>\n

$$\\vec{a}=\\displaystyle\\frac{\\Delta\\vec{v}}{\\Delta t}$$<\/p>\n

$$\\Delta \\vec{v}=\\vec{v}-\\vec{v_0}=\\vec{a}\\cdot\\Delta t$$<\/p>\n

$$\\vec{v}=\\vec{v_0}+\\vec{a}\\cdot\\Delta t$$<\/p>\n

\"26622_p1\"<\/a><\/p>\n

<\/p>\n

\u7531\u6b63\u5f26\u5b9a\u7406\u53ef\u5f97\uff1a<\/p>\n

$$\\displaystyle\\frac{v_0}{\\sin\\left(\\frac{\\pi}{2}+\\varphi\\right)}=\\frac{v_0}{\\sin\\left(\\frac{\\pi}{2}-\\theta\\right)}=\\frac{gt}{\\sin(\\theta-\\varphi)}$$<\/p>\n

\u518d\u4f9d\u7167\u6240\u9700\u6c42\u89e3 $$v$$ \u6216 $$t$$\u3002\u5982\u4e0b\u4f8b\u984c\uff1a<\/p>\n

\u554f\uff1a<\/strong>
\n\u67d0\u7269\u9ad4\u81ea\u5730\u9762\u4ee5\u4ef0\u89d2 $$60^\\circ$$ \u521d\u901f $$20~m\/s$$ \u659c\u9762\u62cb\u51fa\uff0c\u7d93\u6b77\u6642\u9593 $$t$$ \u5f8c\uff0c\u901f\u5ea6\u65b9\u5411\u8207\u6c34\u5e73\u65b9\u5411\u593e\u4fef\u89d2 $$30^\\circ$$\uff0c\u8a66\u6c42\uff1a(1) $$v$$ \u7684\u5927\u5c0f (2) $$t$$\u7684\u5927\u5c0f \uff08$$g = 10~m\/s^2$$\uff09
\n\u7b54\uff1a<\/strong>
\n\u7531\u89d2\u5ea6\u95dc\u4fc2\u53ca\u5404\u7269\u88e1\u91cf\u65b9\u5411\uff0c\u53ef\u7e6a\u51fa\u4ee5\u4e0b\u95dc\u4fc2\u5716<\/p>\n

\"\"<\/a><\/p>\n

\u7531\u6b63\u5f26\u5b9a\u7406\u53ef\u77e5<\/p>\n

$$\\displaystyle\\frac{20}{\\sin 60^\\circ}=\\frac{10\\cdot t}{\\sin 90^\\circ}=\\frac{v}{\\sin 30^\\circ}$$<\/p>\n

    \n
  1. $$\\displaystyle v=\\frac{20}{\\sin60^\\circ}\\cdot\\sin 30^\\circ=\\frac{20}{\\sqrt{3}}=\\frac{20\\sqrt{3}}{3}~(m\/s)$$<\/li>\n
  2. $$\\displaystyle 10\\cdot t=\\frac{20}{\\sin 60^\\circ}\\cdot \\sin 90^\\circ\\Rightarrow{t}=\\frac{2}{\\sqrt{3}\/2}=\\frac{4}{\\sqrt{3}}=\\frac{4\\sqrt{3}}{3}~(s)$$<\/li>\n<\/ol>\n

     <\/p>\n

    2. \u7269\u9ad4\u7684\u4f4d\u79fb $$\\Delta r$$\uff1a<\/span><\/strong><\/p>\n

    \u7531\u52a0\u901f\u5ea6\u7684\u5b9a\u7fa9\u53ef\u5f97 $$\\vec{v}=\\vec{v_0}+\\vec{a}t$$\uff08\u53d6\u51fa\u767c\u6642\u6642\u523b\u70ba\u96f6\uff0c\u51fa\u767c\u9ede\u70ba\u539f\u9ede\uff09\uff0c\u518d\u7531\u901f\u5ea6\u8207\u4f4d\u79fb\u7684\u95dc\u4fc2\u53ef\u5f97\uff1a<\/p>\n

    $$\\displaystyle \\vec{v}=\\frac{d\\vec{r}}{dt}=\\vec{v_0}+\\vec{a}\\cdot t$$<\/p>\n

    $$d\\vec{r}=(\\vec{v_0}+\\vec{a}\\cdot t)dt$$<\/p>\n

    $$\\int d\\vec{r}=\\int\\limits^t_0(\\vec{v_0}+\\vec{a}\\cdot t)dt$$<\/p>\n

    $$\\vec{S}=\\Delta \\vec{r}=(\\vec{v_0}\\cdot t)+(\\frac{1}{2}\\vec{a}\\cdot t^2)$$<\/p>\n

    \u53ef\u5f97\u7269\u9ad4\u6240\u505a\u7684\u4f4d\u79fb\u53ef\u4ee5\u5340\u5206\u70ba $$(\\vec{v_0}\\cdot t)$$ \u5411\u91cf\u8207 $$(\\frac{1}{2}\\vec{a}\\cdot t^2)$$ \u5411\u91cf\u7684\u5408\u6210\uff0c\u5982\u5716<\/p>\n

    \"26622_p2\"<\/a><\/p>\n

    \u518d\u7531\u6b63\u5f26\u5b9a\u7406\u6c42\u89e3\u76f8\u95dc\u7269\u7406\u91cf\uff1a<\/p>\n

    $$\\displaystyle\\frac{v_0\\cdot t}{\\sin(\\frac{\\pi}{2}+\\varphi)}=\\frac{S}{\\sin(\\frac{\\pi}{2}-\\theta)}=\\frac{(\\frac{1}{2}g\\cdot t^2)}{\\sin(\\theta-\\varphi)}$$<\/p>\n

    \u6b64\u4e00\u89e3\u6cd5\u9069\u7528\u65bc\u6c42\u89e3\u659c\u9762\u4e0a\u7684\u62cb\u9ad4\u904b\u52d5\uff0c\u7279\u8209\u4e00\u4f8b\u984c\u5982\u4e0b\uff1a<\/p>\n

    \u554f\uff1a<\/strong>
    \n\u5982\u5716\uff0c\u7403\u5728\u9ad8\u5ea6\u70ba $$20$$ \u7c73\uff0c\u5bec\u5ea6\u70ba $$40$$ \u7c73\u4e4b\u5761\u5e95\uff0c\u4ee5\u521d\u901f $$25$$ \u7c73\uff0f\u79d2\uff0c\u8207\u6c34\u5e73\u593e $$53^\\circ$$ \u4ef0\u89d2\u4e1f\u51fa\uff0c\u5247<\/p>\n

    (1) \u7269\u9ad4\u65bc\u51fa\u767c\u5f8c\u4f55\u6642\u843d\u65bc\u659c\u5761\u9762\uff1f
    \n(2) \u7269\u9ad4\u65bc\u659c\u9762\u4e0a\u7684\u843d\u9ede\u8207\u51fa\u767c\u9ede\u7684\u8ddd\u96e2\uff1f<\/p>\n

    \"\"<\/a><\/p>\n

    \u7b54\uff1a<\/strong><\/p>\n

    \"\"<\/a><\/p>\n

    \u7531\u6b63\u5f26\u5b9a\u7406\u53ef\u5f97\uff1a$$\\displaystyle\\frac{25\\cdot t}{\\sin(90^\\circ+\\varphi)}=\\frac{\\frac{1}{2}\\times{10}t^2}{\\sin(53^\\circ-\\varphi)}=\\frac{S}{\\sin 37^\\circ}$$<\/p>\n

    $$(1)$$ \u7531\u00a0$$\\displaystyle\\frac{25\\cdot t}{\\sin(90^\\circ+\\varphi)}=\\frac{\\frac{1}{2}\\cdot 10t^2}{\\sin(53^\\circ-\\varphi)}$$\uff0c\u5316\u7c21\u53ef\u5f97<\/p>\n

    $$\\displaystyle\\frac{5}{\\cos\\varphi}=\\frac{t}{\\sin(53^\\circ-\\varphi)}$$\uff0c\u5176\u4e2d $$\\displaystyle\\cos\\varphi=\\frac{2}{\\sqrt{5}},~~\\sin\\varphi=\\frac{1}{\\sqrt{5}},~~\\tan\\varphi=\\frac{1}{2}$$<\/p>\n

    $$\\displaystyle t=\\frac{5\\cdot(\\sin(53^\\circ-\\varphi))}{\\cos\\varphi}=\\frac{5(\\sin53^\\circ\\cos\\varphi-\\cos53^\\circ\\sin\\varphi)}{\\cos\\varphi}$$<\/p>\n

    $$\\displaystyle t=5(\\sin53^\\circ-\\cos53^\\circ\\tan\\varphi)=5\\left(\\frac{4}{5}-\\frac{3}{5}\\times\\frac{1}{2}\\right)=2.5~(S)$$<\/p>\n

    $$(2)$$ \u7531 $$\\displaystyle\\frac{25\\cdot t}{\\sin(90^\\circ+\\varphi)}=\\frac{S}{\\sin 37^\\circ}$$\uff0c\u5316\u7c21\u53ef\u5f97<\/p>\n

    $$\\displaystyle S=\\frac{25\\cdot t}{\\cos\\varphi}\\cdot\\sin 37^\\circ=25\\times 2.5\\times \\frac{\\sqrt{5}}{2}\\times \\frac{3}{5}=\\frac{75\\sqrt{5}}{4}~(m)$$<\/p>\n

    \u53c3\u8003\u8cc7\u6599\uff1a
    \n<\/strong>1.\u00a0 \u00a0 \u00a0 \u00a0 \u5357\u4e00\u7248\u7269\u7406(\u4e0a)\u6559\u5e2b\u624b\u518a
    \n2.\u00a0 \u00a0 \u00a0 \u00a0 \u4f8b\u984c\u53d6\u6750\uff1a\u7ff0\u6797\u7248\u984c\u5eab\u7cfb\u7d71<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u5e73\u9762\u7b49\u52a0\u901f\u5ea6\u904b\u52d5\u89e3\u984c\u65b9\u6cd5 \u570b\u7acb\u82d1\u88e1\u9ad8\u7d1a\u4e2d\u5b78\u7269\u7406\u79d1\u8a31\u5bb6\u9298\u8001\u5e2b\/\u570b\u7acb\u5f70\u5316\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb\u6d2a\u9023\u8f1d\u6559\u6388\u8cac\u4efb\u7de8\u8f2f \u4e00\u822c\u800c\u8a00…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,107,3],"tags":[2976,2977],"class_list":["post-26622","post","type-post","status-publish","format-standard","hentry","category-physics01-02","category-physics00","category-physics01","tag-2976","tag-2977","loop-entry","cat-5","cat-107","cat-3","no-thumbnail"],"views":5810,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/26622","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=26622"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/26622\/revisions"}],"predecessor-version":[{"id":88538,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/26622\/revisions\/88538"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=26622"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=26622"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=26622"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}