题目内容
如图6—4所示,河宽为L,船对水的速度为V船,水的流速为V水,试分析:
(1)船怎样渡河,所需时间最短?最短时间为多少?
(2)当V船>V水时,船怎样渡河位移最小?最小位移是多少?
(3)当V水<V船时,船怎样渡河位移最小?最小位移是多少?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241153146612049.gif)
(1)船怎样渡河,所需时间最短?最短时间为多少?
(2)当V船>V水时,船怎样渡河位移最小?最小位移是多少?
(3)当V水<V船时,船怎样渡河位移最小?最小位移是多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241153146612049.gif)
(1)船头垂直于河岸,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314676442.gif)
(2)船头与河岸上游夹角为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314692521.gif)
(3)船头与河岸上游夹角为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314707648.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314676442.gif)
(2)船头与河岸上游夹角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314692521.gif)
(3)船头与河岸上游夹角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314707648.gif)
(1)船渡河的时间t取决于V船垂直于河岸的分量Vy和河宽L,而与V水无关。设船头与河岸的夹角为θ,则渡河时间可以表示为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314707599.gif)
可见,当sinθ=1,θ=90º即船头垂直河岸时,如图6—5所示渡河时间最短![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314723430.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241153147392343.gif)
(2)如图6—6所示,当V船>V水时,船的合速度v垂直河岸时,渡河位移最小,且等于河宽,即Smin=L,所以船头应斜对上游,且河岸的夹角为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314754776.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241153147702160.gif)
(3)如图6—7所示,当V水<V船时,以V水末端为圆心,以V船大小为半径画半圆,船的实际速度为以V水的始端为始端,以圆周上一点为末端的矢量。其中与河岸的夹角最大的方向,即沿图示切线方向时,渡河路径最短。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241153147851037.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241153148013162.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314707599.gif)
可见,当sinθ=1,θ=90º即船头垂直河岸时,如图6—5所示渡河时间最短
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314723430.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241153147392343.gif)
(2)如图6—6所示,当V船>V水时,船的合速度v垂直河岸时,渡河位移最小,且等于河宽,即Smin=L,所以船头应斜对上游,且河岸的夹角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115314754776.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241153147702160.gif)
(3)如图6—7所示,当V水<V船时,以V水末端为圆心,以V船大小为半径画半圆,船的实际速度为以V水的始端为始端,以圆周上一点为末端的矢量。其中与河岸的夹角最大的方向,即沿图示切线方向时,渡河路径最短。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241153147851037.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241153148013162.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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