题目内容
如图所示,光滑水平面上有两辆车,甲车上面有发射装置,甲车连同发射装置质量M1=1kg,车上另有一个质量为m=0.2kg的小球。甲车静止在平面上, 乙车以V0=8m/s的速度向甲车运动,乙车上有接收装置,总质量M2=2kg,问:甲车至少以多大的水平速度将小球发射到乙车上,两车才会相撞?(球最终停在乙车上)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241343041431660.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241343041431660.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134304175346.png)
要使两车不相撞,则两车速度相等,速度设为V,
以三者为系统,动量守恒,
解得 V=5m/s
以球与乙车为系统,设小球的发射速度为
,由动量守恒:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134304284972.png)
解得
=25m/s
以三者为系统,动量守恒,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241343042061013.png)
以球与乙车为系统,设小球的发射速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134304175346.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134304284972.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134304175346.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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