名校
1 . 如图河堤横断面迎水坡
的坡比
, 堤高
,则坡面
的长度是( )m
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5881f1ce9b4172ca346032d0fd1e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e604056e427f82f7a282e8ad3d14e636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.8 | B.18 | C.![]() | D.![]() |
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2 . 在坡度为
的斜坡与水平地面的纵向截面图上,建立如图所示的平面直角坐标系.已知点
在斜坡上,
,从点
向右发射出的小球沿抛物线
运动,解决下列问题.
的坐标是__________;
(2)①求
所满足的数量关系;
②当小球恰好落到原点时,求抛物线的函数表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60fe5130254a1d38bb4fd0015630f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318b6a044f8009271b165dc7e2cca404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18269e4b2c08f69b719c4c7e7d71733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc2ac0d7b8a2d9c539588a3a7e3791c.png)
②当小球恰好落到原点时,求抛物线的函数表达式.
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3 . 某兴趣小组为测量其所在城市同一水平面上的高铁东站和高铁西站之间的距离,将无人机停在空中M处,测得高铁西站所在的A处的俯角为
,再将无人机沿坡度为
的方向飞行2千米到达N处,此时测得A处的俯角为
,高铁东站所在的B处的俯角为
(点A、B、M、N在同一竖直平面内),求
之间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe51dcd5ae4e861929d637ca20124928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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4 . 城市规划期间,欲拆除一电线杆
,如图,已知距电线杆
的水平距离
的D处有一大坝,背水坡
的坡度
,坝高
为
,在坝顶点C处测得电线杆顶点A的仰角为
,
之间是宽为
的行人道,试问在拆除电线杆
时,为确保行人安全,是否需要将此人行道封上?(提示:在地面上,以点B为圆心,以
为半径的圆形区域为危险区域)(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6300ce2ba6dd715e02511e173f4c56fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bbf35fe2349c32441815e225ef129f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71a41641aa0d0e45a3c03d3d2c1196b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71a41641aa0d0e45a3c03d3d2c1196b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460317e7c26f95b9b29cfe1a89b796d6.png)
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2024-05-24更新
|
266次组卷
|
3卷引用:2023年山东省 潍坊市 青州市 中考数学模拟预测题
5 . 如图
所示为
年
月
日我国陆军进行军事训练的一幕,全体官兵士气高昂,精神饱满.图
所示为训练中远程火炮射击的简图.已知一门炮筒长约
的远程火炮位于
点,
点为炮口,火炮
与水平地面夹角约为
.此时火炮进行了一次射击,炮弹在飞行后落在了斜坡
上.已知
的坡角为
,炮弹的轨迹为圆弧,炮弹轨迹所对的圆的圆心恰为点
,
,斜坡的高
,则:
的半径;
(2)如图
,在炮弹发射的同时,我军某参演部队检测到了炮弹,并自斜坡上射出一发拦截弹,已知发射点
距坡底为
,射出拦截弹的轨迹为直线且与水平方向夹角为
.拦截弹恰好于
点成功拦截炮弹.若拦截弹的速度约为
,炮弹的速度约为
,则求炮弹飞过的路径长.(结果取整数.参考数据:
,
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e8936c9fe1e81726455908657a29fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c758c27bec97c234d1d818c40f3d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83042953e7f15e984b2da2ee9ca678d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83042953e7f15e984b2da2ee9ca678d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8141d00b74eb4c50bf861e6ff0edf137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafd0f58094e8863aa5cb0bef4bed25e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc3eb8269579cbe19b1adbfb3e225733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
(2)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c758c27bec97c234d1d818c40f3d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f25cd21af818ad98b6d9f023ba285f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ccab58a182c96268b0fc987c3edbf18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0701b3b16fdef6eb2a21a03311faa0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc714fe6656552ae227332550756a620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90b8e784cfcf697083f5a1bef0baa7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8639b0b48393b0a99719216160822336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bbe1e9efd3671d504a2144e22e51fe.png)
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6 . 小明在一段斜坡
上进行跑步训练.在训练过程中,始终有一架无人机在小明正上方随他一起运动,无人机速度为
,距水平地面的高度总为
(在直线
上运动).现就小明训练中部分路段作出如图函数图象:已知
点坐标是
,斜坡
的坡角为
.
上的跑步速度.
(2)求
段
关于
的函数解析式;
(3)若小明沿
方向运动,求无人机与小明之间距离不超过
的时长.(参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f037cf514f9f12ec2f7ad6eb409856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbae9b64d5a3a42931dc41c32fc4bb75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b749f9acb5f0de709a1709bbdd42614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c6efd24d7b6da440b81b75166bbf80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce6c3d6874f9c06e693b64b2b40d610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe53cbaa36cecf802efc9e81e9937ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若小明沿
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5e1433d7c2ad6a5b2de8a557a43d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e6e41ac221847824a72e964f340f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0af7b2d62b94466387c8a15ab0b7350a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d57ac09088f0dbed7e217d2a9bc037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7730adb728a84231d6a03c6d88779504.png)
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7 . 如图是某货站传送货物的平面示意图,为了提高传送过程的安全性,工人师傅欲减小传送带与地面的夹角,使其由
改为
,已知原传送带
长为4米.(计算结果精确到0.1米,参考数据:
,
,
,
,
,
)
的长度.
(2)如果需要在货物着地点C的左侧留出2米的通道,试判断距离B点4米的货物
是否需要挪走,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36581140ebac5d28438ea63b1b23b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31a14bd2a972f43d7a26a99589ad083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94389d0f199119e43d35bc6249f1a14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a3e48a63eb65952fbf9bf39c590ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d995a8af067807d765133a2436cad7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3097c385f3421e457f9232690ad0dc16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ae32a2c3ce860153288435be492e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f441d98ac4f433d3aab3b2e4111d86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)如果需要在货物着地点C的左侧留出2米的通道,试判断距离B点4米的货物
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db492efc6bfe199d47633e6d5946ad57.png)
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8 . 如图,在坡度为
的山坡上种树,已知
,相邻两树
的坡面距离为10米,则两树的水平距离
为__________ 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2450156c6f081864f1efcf10af156e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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9 . 小明沿着坡度
的斜坡向上行走了26米,则他距离地面的垂直高度升高了______ 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1852175af2bff405159bc6b574dcb9f.png)
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10 . 如图,在坡比为
的斜坡上有一电线杆
.某时刻身高1.7米的小明在水平地面上的影长恰好与其身高相等,此时电线杆在斜坡上的影长
为30米,则电线杆
的高为( )米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db20862b954cd1886f4765657a46d91c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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