题目内容
如图所示是伦敦奥运会期间水上运动中心安置在游泳池底部的照相机拍摄的一张照片,相机的镜头竖直向上.照片中,水立方运动馆的景象呈现在半径
的圆形范围内,水面上的运动员手到脚的长度
.若已知水的折射率
,运动员的实际身高
,请计算该游泳池的水深H。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241722202706480.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172219100532.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172219319521.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172219553453.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172219818557.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241722202706480.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172220536455.png)
试题分析:设照片圆形区域的实际半径为R,如图所示.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241722209264416.jpg)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172220941748.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172221160542.png)
几何关系
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172221581842.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172222064583.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172222283762.png)
代入数据,解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172222595854.png)
点评:本题为估算题,在取运动员实际长度时可以有一个范围,但要符合实际,故求得h值可以不同
![](http://thumb2018.1010pic.com/images/loading.gif)
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