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\u4e00\u3001\u4e8c\u6b21\u65b9\u7a0b\u7684\u5224\u522b\u5f0f
\n\u9009\u53d6\u9002\u5f53\u7684\u7269\u7406\u91cf\uff0c\u901a\u8fc7\u7b49\u5f0f\u53d8\u6362\u51fa\u73b0\u4e8c\u6b21\u9879\uff0c\u518d\u5229\u7528\u5224\u522b\u5f0f$$\\Delta=b^2-4ac\\geq0$$\u4f5c\u4e3a\u6709\u89e3\u7684\u6761\u4ef6\u6765\u6c42\u89e3\u3002<\/p>\n
\u4e8c\u3001\u4e8c\u6b21\u51fd\u6570\u7684\u914d\u65b9\u6cd5
\n\u5bf9\u4e8e\u4e8c\u6b21\u51fd\u6570$$y=ax^2+bx+c=a(x+\\frac{b}{2a})^2+\\frac{4ac-b^2}{4a}$$
\n\u82e5a<0\uff0c\u5219y\u6709\u6781\u5927\u503c\uff0c\u5f53$$x=-\\frac{b}{2a}$$\u65f6\uff0c$$y_{max}=\\frac{4ac-b^2}{4a}$$\uff1b
\n\u82e5a>0\uff0c\u5219y\u6709\u6781\u5c0f\u503c\uff0c\u5f53$$x=-\\frac{b}{2a}$$\u65f6\uff0c$$y_{min}=\\frac{4ac-b^2}{4a}$$<\/p>\n
\u9898\u5982\u5300\u52a0\u901f\u4e0e\u5300\u901f\u8fd0\u52a8\u7684\u8ffd\u51fb\u95ee\u9898\u3002
\n\u6c7d\u8f66\u5728\u8def\u53e3\u4ee5$$3m\/s^2$$ \u7684\u52a0\u901f\u5ea6\u5f00\u59cb\u884c\u9a76\uff0c\u6b64\u65f6\u6070\u6709\u4e00\u8f86\u81ea\u884c\u8f66\u4ee56$$m\/s$$\u7684\u901f\u5ea6\u5300\u901f\u9a76\u8d85\u8fc7\u6c7d\u8f66\u3002\u6c7d\u8f66\u4ece\u8def\u53e3\u5f00\u52a8\u540e\uff0c\u5728\u8ffd\u4e0a\u81ea\u884c\u8f66\u4e4b\u524d\u8fc7\u591a\u957f\u65f6\u95f4\u4e24\u8f66\u76f8\u8ddd\u6700\u8fdc\uff1f\uff082s\uff0c6m\uff09<\/p>\n
\u4e09\u3001\u5229\u7528\u4e0d\u7b49\u5f0f
\n1.$$A+B\\geq2\\sqrt{AB}$$\uff1a\u5bf9\u6b63\u6570A\u548cB\uff0c\u82e5AB\u4e3a\u5e38\u6570\uff0c\u5f53A=B\u65f6\uff0cA\u548cB\u7684\u548c\u6709\u6700\u5c0f\u503c\u3002
\n2.$$AB\\leq(\\frac{A+B}{2})^2$$\uff1a\u5bf9\u6b63\u6570A\u548cB\uff0c\u82e5A+B\u4e3a\u5e38\u6570\uff0c\u5f53A=B\u65f6\uff0cA\u548cB\u7684\u548c\u6709\u6700\u5927\u503c\u3002
\n\u7c7b\u4f3c\u8fd8\u6709$$A+B+C\\geq3\\sqrt[3]{ABC}$$<\/p>\n
\u9898\u5982\u6c34\u5e73\u91ca\u653e\u60ac\u6302\u5c0f\u7403\u91cd\u529b\u6700\u5927\u529f\u7387\u4f4d\u7f6e\u6c42\u89e3\u3002
\n\u4e00\u8f7b\u7ef3\u4e00\u7aef\u56fa\u5b9a\uff0c\u53e6\u4e00\u7aef\u62f4\u4e00\u5c0f\u7403\uff0c\u62c9\u8d77\u5c0f\u7403\u4f7f\u8f7b\u7ef3\u6c34\u5e73\u540e\u65e0\u521d\u901f\u5ea6\u7684\u91ca\u653e\uff0c\u5c0f\u7403\u5728\u8fd0\u52a8\u81f3\u8f7b\u7ef3\u8fbe\u5230\u7ad6\u76f4\u4f4d\u7f6e\u7684\u8fc7\u7a0b\u4e2d\uff0c\u5c0f\u7403\u6240\u53d7\u91cd\u529b\u7684\u77ac\u65f6\u529f\u7387\u5728\u4f55\u5904\u53d6\u5f97\u6700\u5927\u503c\uff1f
\n\uff08$$cos\\theta=\\frac{\\sqrt3}{3}$$\uff0c$$\\theta$$\u4e3a\u7ebf\u4e0e\u7ad6\u76f4\u65b9\u5411\u7684\u5939\u89d2\u3002\uff09
\n\u6b64\u9898\u76ee\u4e5f\u53ef\u4ee5\u7814\u7a76\u7ad6\u76f4\u65b9\u5411\u7684\u53d7\u529b\u60c5\u51b5\uff0c
\n\u5f53$$a_{y}=0$$\u65f6\u7ad6\u76f4\u65b9\u5411\u7684\u901f\u5ea6\uff08$$V_{y}=Vcos\\theta$$\uff09\u6700\u5927\uff0c\u5219$$P_{G}=MgVcos\\theta$$\u53d6\u6700\u5927\u503c\u3002<\/p>\n
\u56db\u3001\u4e09\u89d2\u51fd\u6570
\n\u7b80\u5355\u4e00\u70b9\u7684\u6bd4\u5982$$y=Asin\\alpha\\cdot{cos\\alpha}=$$$$\\frac{1}{2}Asin2\\alpha$$\uff0c\u5f53$$\\alpha=\\frac{\\pi}{2}$$\u53d6\u6781\u503c\u3002
\n\u5982\u5728\u5e95\u8fb9\u5b9a\u957f\u5149\u6ed1\u659c\u9762\u4e0b\u6ed1\u65f6\u95f4\u6781\u503c\u6c42\u89e3\u3002
\n\u5982\u659c\u9762\u5e95\u8fb9\u6052\u5b9a\u4e3ad\uff0c\u5f53\u659c\u9762\u4e0e\u5e95\u8fb9\u6240\u6210\u5939\u89d2\u03b8\u4e3a\u591a\u5927\u65f6\uff0c\u7269\u4f53\u6cbf\u6b64\u5149\u6ed1\u659c\u9762\u7531\u9759\u6b62\u4ece\u9876\u7aef\u6ed1\u5230\u5e95\u7aef\u6240\u7528\u65f6\u95f4\u6700\u77ed? \uff08$$\\theta=\\frac{\\pi}{4}$$\uff0c$$t_{min}=\\surd{\\frac{4d}{g}}$$\uff09<\/p>\n
\u5bf9y\u5173\u4e8e$$\\alpha$$\u7684\u51fd\u6570\uff0c$$y=asin\\alpha+bcos\\alpha$$\uff0c\u4ee4$$sin\\beta=\\frac{b}{\\surd{a^2+b^2}}$$\uff0c$$cos\\beta=\\frac{a}{\\surd{a^2+b^2}}$$
\n\u5219\u6709$$y=\\sqrt{a^2+b^2}sin(\\alpha+\\beta)\\leq\\sqrt{a^2+b^2}$$\uff0c\u5f53$$\\alpha=arcsin\\frac{a}{\\surd{a^2+b^2}}$$\u65f6\u53d6\u7b49\u3002<\/p>\n
\u9898\u5982\u7269\u4f53\u653e\u7f6e\u5728\u6c34\u5e73\u5730\u9762\u4e0a\uff0c\u4e0e\u5730\u9762\u4e4b\u95f4\u7684\u52a8\u6469\u64e6\u56e0\u6570\u4e3a\u03bc\uff0c\u7269\u4f53\u91cd\u4e3aG\uff0c\u6b32\u4f7f\u7269\u4f53\u6cbf\u6c34\u5e73\u5730\u9762\u505a\u5300\u901f\u76f4\u7ebf\u8fd0\u52a8\uff0c\u6240\u7528\u7684\u6700\u5c0f\u62c9\u529bF\u4e3a\u591a\u5927\uff1f
\n\uff08$$tan\\theta=\\frac{1}{\\mu}$$\uff0c$$F_{min}=\\frac{\\mu}{\\surd{1+\\mu^2}}G$$\uff09<\/p>\n
\u4e94\u3001\u77e2\u91cf\u4e09\u89d2\u5f62
\n\u67d0\u4e00\u5206\u529b$$F_{1}$$\u5927\u5c0f\u548c\u65b9\u5411\u5b9a\u503c\uff0c\u5408\u529bF\u7684\u65b9\u5411\u56fa\u5b9a\uff0c\u5219\u53e6\u5916\u4e00\u5206\u529b\u6709\u6700\u5c0f\u503c\uff0c$$F_2\\geq{F_1sin\\alpha}$$
\n\u9898\u5982\u4e0a\u9762\u7c97\u7cd9\u6c34\u5e73\u9762\u5300\u901f\u8fd0\u52a8\u7269\u4f53\u6240\u6536\u5916\u529b\u7684\u6781\u503c\u95ee\u9898\u6c42\u89e3\u4e5f\u53ef\u4ee5\u501f\u9274\u6b64\u6cd5\u3002<\/p>\n
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\n\u6bd4\u5982\u5bf9\u4e8c\u6b21\u51fd\u6570$$y=ax^2+bx+c$$\uff0c$$y’=2ax+b=0$$\uff0c$$x=-\\frac{b}{2a}$$\u65f6\u51fd\u6570\u53d6\u6781\u503c\u3002
\n\u5982\u7b49\u91cf\u540c\u79cd\u7535\u8377\u4e2d\u5782\u7ebf\u4e0a\u573a\u5f3a\u6781\u5927\u4f4d\u7f6e\u7684\u6c42\u89e3\u3002
\n\u5bf9\u6240\u5f97\u5230\u5f97\u51fd\u6570\u5173\u4e8e$$sin\\theta$$\u6c42\u5bfc\u53ef\u5f97\uff0c\u5f53$$\\theta=arcsin\\frac{\\sqrt{3}}{3}$$\u65f6\u53d6\u6781\u5927\u503c\uff0c$$\\theta$$\u4e3a\u7535\u8377\u4e0eP\u70b9\u8fde\u7ebf\u4e0e\u6c34\u5e73\u65b9\u5411\u7684\u5939\u89d2\u3002\uff09
\n…
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