题目内容
地面上有一个半径为R的圆形跑道,高为h的平台边缘上的P点在地面上P′点的正上方,P′与跑道圆心O的距离为L(L>R),如图所示。跑道上停有一辆小车,现从P点水平抛出小沙袋,使其落入小车中(沙袋所受空气阻力不计)。问:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500515427812639.png)
(1)若小车在跑道上运动,则沙袋被抛出时的初速度在什么范围内?
(2)若小车沿跑道顺时针做匀速圆周运动,当小车恰好经过A点时,将沙袋抛出,为使沙袋能在B处落入小车中,小车的速率v应满足什么条件?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500515427812639.png)
(1)若小车在跑道上运动,则沙袋被抛出时的初速度在什么范围内?
(2)若小车沿跑道顺时针做匀速圆周运动,当小车恰好经过A点时,将沙袋抛出,为使沙袋能在B处落入小车中,小车的速率v应满足什么条件?
(1)
;(2)
(n=0,1,2,3……)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051542931123.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051543091028.png)
试题分析:(1)沙袋从P点被抛出后做平抛运动,设它的落地时间为t,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005154325650.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005154356675.png)
若小车在跑道上运动,要使沙袋落入小车,最小的抛出速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051543711204.png)
若当小车经过C点时沙袋刚好落入,抛出时的初速度最大,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005154387795.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051544031119.png)
所以沙袋被抛出时的初速度范围为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051542931123.png)
(2)要使沙袋能在B处落入小车中,小车运动的时间应与沙袋下落和时间相同
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051544491042.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005154481771.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051543091028.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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