题目内容
A球自距地面高h处开始自由下落,同时B球以初速度v0正对A球竖直上抛,空气阻力不计。问:
(1)要使两球在B球上升过程中相遇,则v0应满足什么条件??
(2)要使两球在B球下降过程中相遇,则v0应满足什么条件?
(1)要使两球在B球上升过程中相遇,则v0应满足什么条件??
(2)要使两球在B球下降过程中相遇,则v0应满足什么条件?
(1)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820514454.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820529657.gif)
两球相遇时位移之和等于h。即:
?所以:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820607405.gif)
而B球上升的时间:
,B球在空中运动的总时间:
?
(1)欲使两球在B球上升过程中相遇,则有
t<t1,即
,所以 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820514454.gif)
(2)欲使两球在B球下降过程中相遇,则有:?
t1<t<t2
即:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820841606.gif)
所以:
?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820592740.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820607405.gif)
而B球上升的时间:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820623306.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820654448.gif)
(1)欲使两球在B球上升过程中相遇,则有
t<t1,即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820732475.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820514454.gif)
(2)欲使两球在B球下降过程中相遇,则有:?
t1<t<t2
即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820841606.gif)
所以:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113820529657.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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