这个冬天,冰雪旅游成为了文旅市场的主要增长点.如图,这是某滑雪场滑雪大跳台的简化模型.
段和
段是长度均为
的倾斜滑道,
段为圆弧滑道,与
段平滑连接,
段为结束区.滑雪爱好者们从助滑区
段的台端A点出发,在助滑区
段上获得高速度,至跳台区
段依靠惯性并配合身体动作跃向空中,从跳台区的末端C点水平飞出后,身体以C为顶点的抛物线轨迹在空中飞行.已知跳台高
为
,某位滑雪爱好者的一次动作中,当离开跳台末端C点后水平前进了
时,高度恰好下降了
(忽略运动过程中所受的空气阻力),为方便研究,我们建立了以跳台底端F为原点,跳台
所在直线为y轴的平面直角坐标系.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/28/e28d1e86-0c04-4620-bc94-7d994b29bc0c.png?resizew=265)
(1)请求出该滑雪爱好者此次动作中运动轨迹所对应的抛物线的函数解析式;
(2)若在着陆区斜坡
段上着陆,则可以利用斜坡的角度进行有效的缓冲;若在终点区
段上着陆,则会增加受伤的风险.请判断这位滑雪爱好者此次动作会在哪个区域着陆,并说明理由.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f631cfdf4666db95beb923072ced8d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8badcdb1e5621f0ac4d9272041185a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1611d15c7e1e4ab4a4a61537b3989d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e6e41ac221847824a72e964f340f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8120f2eeb724c756b5f84a14c6df527.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/28/e28d1e86-0c04-4620-bc94-7d994b29bc0c.png?resizew=265)
(1)请求出该滑雪爱好者此次动作中运动轨迹所对应的抛物线的函数解析式;
(2)若在着陆区斜坡
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb015b3adfab424c91f1ed8b123fc23c.png)
更新时间:2024-03-28 23:03:35
|
【知识点】 图形问题(实际问题与二次函数)
相似题推荐
解答题-证明题
|
适中
(0.65)
【推荐1】如图,已知锐角三角形
,点A在三角形内,
,
,
.作
的外接圆
,交
于点F,连接
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/afdbeecc-917e-43e1-9b5f-2be956104cdc.png?resizew=132)
(1)求证:
.
(2)若
,
,
①求
的取值范围.
②求
的面积S的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b03bf58cba56d1b98a8a457982870b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df96f073bbcf475cf3a4e2b3b7c7edf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30e50e094cd2849e38859b36aad0b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ccea461315a9d05aa0193b937d4bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/afdbeecc-917e-43e1-9b5f-2be956104cdc.png?resizew=132)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916aa68e47334ba3b95cd7d99f67c6b3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedd51383f8f047f565191b128cec637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7aafc14893896f4f908f2deb53c9f65.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ccea461315a9d05aa0193b937d4bfe.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
名校
【推荐2】已知
和
(
<
)是抛物线
的函数图象与x轴两个交点A,B的横坐标,我们把
称为横交距.
(1)已知
,则横交距d=_______.
(2)已知抛物线
,当横交距
时,求c的值.
(3)已知抛物线
经过点A(1,0),且与y轴交于点C,若存在横交距d,连接AC,BC,使其△ABC面积为S,请直接写出当
时c的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6337d68cd5653767e3a1889b8b2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8821f33f1fc7aeeb3403801a831b0b.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d06047c922454151df55024d4bfef82.png)
(2)已知抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe0eae89f0d8d152ae5a8840419822d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c1344592c925b273f2cb9b9e47ebbb.png)
(3)已知抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78bbcb52d0120d28c603cba93c0b5764.png)
您最近一年使用:0次