题目内容
某人横渡一河流,船划行速度和水流动速度一定,此人过河最短时间为t1;若此船用最短的位移过河,则需时间为t2,若船速大于水速,则船速与水速之比为:( )
A.![]() | B.![]() | C.![]() | D.![]() |
A
试题分析:设河宽为d,垂直河岸过河最短时间过河:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191234308519.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191234698546.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241912349784456.jpg)
最短位移过河时,合位移垂直河岸,如图所示,故有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191235025645.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191235322767.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191235696851.png)
所以:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191236102768.png)
点评:小船过河问题的处理只需要将运动分解到沿河方向和垂直河岸方向,分别列式即可.注意:(1)当船速垂直河岸时,用时最少;(2)当船速大于水速时,合速度垂直河岸,位移最小.
![](http://thumb2018.1010pic.com/images/loading.gif)
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