题目内容
某跳水运动员在一次跳水训练时的跳水曲线为如图所示的抛物线一段,已知跳水板
长为2m,跳水板距水面
的高
为3m,
=5m,
=6m,为安全和空中姿态优美,训练时跳水曲线应在离起跳点
m(
)时达到距水面最大高度4m,规定:以
为横轴,
为纵轴建立直角坐标系.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240227234473304.png)
(1)当
=1时,求跳水曲线所在的抛物线方程;
(2)若跳水运动员在区域
内入水时才能达到压水花的训练要求,求达到压水花的训练要求时
的取值范围.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723323396.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723338405.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723338398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723354414.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723369403.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723385313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723401405.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723338405.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723432391.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240227234473304.png)
(1)当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723385313.png)
(2)若跳水运动员在区域
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723479386.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723385313.png)
(1)
;(2)
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723510716.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723525469.png)
试题分析:(1)由题意可以将抛物线的方程设为顶点式.由顶点(3,4),然后代入点
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723541545.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723541545.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723650500.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723666283.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723385313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723479386.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723713898.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240227237281624.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723744536.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723775545.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723385313.png)
试题解析:(1)由题意知最高点为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723806601.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723822404.png)
设抛物线方程为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723837934.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723853377.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723869766.png)
将
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723541545.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723884715.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723915346.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723931195.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723853377.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723510716.png)
(2)将点
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723541545.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723837934.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723650500.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022724025549.png)
由题意,方程
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723713898.png)
令
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240227240561557.png)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240227240711079.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240227240711089.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022724087603.png)
达到压水花的训练要求时
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723385313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824022723525469.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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