修改021804,018517,009641,021827:021828题面及答案
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@ -271613,7 +271613,7 @@
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"009641": {
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"id": "009641",
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"content": "已知两个力(单位: $\\text{N}$)$\\overrightarrow{f_1}$与$\\overrightarrow{f_2}$的夹角为$60^\\circ$, 其中$\\overrightarrow{f_1}=(2, 0)$. 某质点在这两个力的共同作用下, 由点$A(1, 1)$移动至点$B(6, 6)$(单位: \\text{m}).\\\\\n(1) 求$\\overrightarrow{f_2}$;\\\\\n(2) 求$\\overrightarrow{f_1}$与$\\overrightarrow{f_2}$的合力对质点所做的功.",
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"content": "已知两个力(单位: $\\text{N}$)$\\overrightarrow{f_1}$与$\\overrightarrow{f_2}$的夹角为$60^\\circ$, 其中$\\overrightarrow{f_1}=(2, 0)$. 某质点在这两个力的共同作用下, 从静止起, 由点$A(1, 1)$移动至点$B(6, 6)$(单位: \\text{m}).\\\\\n(1) 求$\\overrightarrow{f_2}$;\\\\\n(2) 求$\\overrightarrow{f_1}$与$\\overrightarrow{f_2}$的合力对质点所做的功.",
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"objs": [],
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"tags": [
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"第五单元"
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@ -271625,7 +271625,8 @@
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"usages": [],
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"origin": "新教材必修第二册课堂练习",
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"edit": [
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"20220730\t王伟叶"
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"20220730\t王伟叶",
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"20240224\t王伟叶"
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],
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"same": [
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"016175"
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@ -501547,7 +501548,7 @@
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},
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"018517": {
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"id": "018517",
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"content": "将质量为$20 \\mathrm{kg}$的物体用两根绳子悬挂起来, 如图, 两根绳子与铅锤线的夹角分别为$45^{\\circ}$与$30^{\\circ}$, 求它们分别提供的拉力的大小. (结果精确到$0.1 \\mathrm{N}$)\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) coordinate (O);\n\\draw (O) ++ ({-2/sqrt(3)},2) coordinate (S) (O) ++ (2,2) coordinate (T);\n\\draw ($(S)!-0.2!(T)$) -- ($(T)!-0.2!(S)$);\n\\draw (S)--(O)--(T);\n\\draw [->] (O) --++ (120:2) node [left] {$\\overrightarrow{f_1}$};\n\\draw [->] (O) --++ (1,1) node [right] {$\\overrightarrow{f_2}$};\n\\draw [dashed] (O) --++ (0,2) coordinate (P);\n\\draw pic [\"$30^\\circ$\", angle eccentricity = 2.5] {angle = P--O--S};\n\\draw pic [\"$45^\\circ$\", angle eccentricity = 2] {angle = T--O--P};\n\\draw (O) -- (0,-0.5) coordinate (A);\n\\draw (A) ++ (-0.3,-0.6) rectangle++ (0.6,0.6);\n\\draw (A) ++ (0.3,-0.3) node [right] {$20$kg};\n\\end{tikzpicture}\n\\end{center}",
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"content": "将质量为$20 \\mathrm{kg}$的物体用两根绳子悬挂起来, 如图, 两根绳子与铅垂线的夹角分别为$45^{\\circ}$与$30^{\\circ}$, 求它们分别提供的拉力的大小. (结果精确到$0.1 \\mathrm{N}$)\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) coordinate (O);\n\\draw (O) ++ ({-2/sqrt(3)},2) coordinate (S) (O) ++ (2,2) coordinate (T);\n\\draw ($(S)!-0.2!(T)$) -- ($(T)!-0.2!(S)$);\n\\draw (S)--(O)--(T);\n\\draw [->] (O) --++ (120:2) node [left] {$\\overrightarrow{f_1}$};\n\\draw [->] (O) --++ (1,1) node [right] {$\\overrightarrow{f_2}$};\n\\draw [dashed] (O) --++ (0,2) coordinate (P);\n\\draw pic [\"$30^\\circ$\", angle eccentricity = 2.5] {angle = P--O--S};\n\\draw pic [\"$45^\\circ$\", angle eccentricity = 2] {angle = T--O--P};\n\\draw (O) -- (0,-0.5) coordinate (A);\n\\draw (A) ++ (-0.3,-0.6) rectangle++ (0.6,0.6);\n\\draw (A) ++ (0.3,-0.3) node [right] {$20$kg};\n\\end{tikzpicture}\n\\end{center}",
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"objs": [],
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"tags": [
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"第五单元"
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@ -501559,7 +501560,8 @@
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"usages": [],
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"origin": "空中课堂必修第二册平面向量例题与习题",
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"edit": [
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"20230705\t王伟叶"
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"20230705\t王伟叶",
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"20240224\t王伟叶"
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],
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"same": [],
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"related": [],
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@ -593816,7 +593818,7 @@
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"第五单元"
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],
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"genre": "填空题",
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"ans": "$(-2,1)$",
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"ans": "$(-2,-1)$",
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"solution": "",
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"duration": -1,
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"usages": [
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@ -593831,7 +593833,8 @@
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],
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"origin": "2025届高一下校本作业",
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"edit": [
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"20230209\t王伟叶"
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"20230209\t王伟叶",
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"20240224\t王伟叶"
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],
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"same": [],
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"related": [],
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@ -594539,7 +594542,7 @@
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},
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"021827": {
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"id": "021827",
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"content": "已知$\\triangle ABC$的重心为$G$, $O$为三角形外的任一点, $\\overrightarrow{OA}=\\overrightarrow {a}$, $\\overrightarrow{OB}=\\overrightarrow {b}$, $\\overrightarrow{OC}=\\overrightarrow {c}$, 试用$\\overrightarrow {a}$、$\\overrightarrow {b}$、$\\overrightarrow {c}$表示$\\overrightarrow{OG}$\\blank{50}.",
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"content": "已知$\\triangle ABC$的重心为$G$, $O$为三角形外的任一点, $\\overrightarrow{OA}=\\overrightarrow {a}$, $\\overrightarrow{OB}=\\overrightarrow {b}$, $\\overrightarrow{OC}=\\overrightarrow {c}$, 试用$\\overrightarrow {a}$、$\\overrightarrow {b}$、$\\overrightarrow {c}$表示$\\overrightarrow{OG}$, $\\overrightarrow{OG}=$\\blank{50}.",
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"objs": [],
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"tags": [
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"第五单元"
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@ -594561,7 +594564,8 @@
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],
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"origin": "2025届高一下校本作业",
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"edit": [
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"20230209\t王伟叶"
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"20230209\t王伟叶",
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"20240224\t王伟叶"
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],
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"same": [],
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"related": [],
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@ -594577,7 +594581,7 @@
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"第五单元"
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],
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"genre": "解答题",
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"ans": "(1) 当$x=\\dfrac{43}{29}$时，最大值为$\\sqrt{319}$;\\\\\n(2) 当$x=2$时，最小值为$4*\\sqrt{2}$;\\\\\n(3) 当$x=\\dfrac{2}{3}$时，最大值为$5$.",
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"ans": "(1) 当$x=\\dfrac{43}{29}$时，最大值为$\\sqrt{319}$;\\\\\n(2) 当$x=2$时，最小值为$4\\sqrt{2}$;\\\\\n(3) 当$x=\\dfrac{2}{3}$时，最大值为$5$.",
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"solution": "",
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"duration": -1,
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"usages": [
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@ -594593,7 +594597,8 @@
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],
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"origin": "2025届高一下校本作业",
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"edit": [
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"20230209\t王伟叶"
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"20230209\t王伟叶",
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"20240224\t王伟叶"
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],
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"same": [],
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"related": [],
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