题目内容
参加电视台娱乐节目,选手要从较高的平台上以水平速度跃出后,落在水平传送带上,已知平台与传送带高度差H=1.8 m,水池宽度x0=1.2 m,传送带A、B间的距离L0=20 m,由于传送带足够粗糙,假设人落到传送带上后瞬间相对传送带静止,经过一个Δt=1.0 s反应时间后,立刻以a=2 m/s2恒定向右加速度跑至传送带最右端.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242142197054441.jpg)
(1)若传送带静止,选手以v0=3 m/s水平速度从平台跃出,求从开始跃出到跑至传送带右端经历的时间.
(2)若传送带以u=1 m/s的恒定速度向左运动,选手要能到达传送带右端,他从高台上跃出的水平速度v1至少多大?在此情况下到达B点时速度大小是多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242142197054441.jpg)
(1)若传送带静止,选手以v0=3 m/s水平速度从平台跃出,求从开始跃出到跑至传送带右端经历的时间.
(2)若传送带以u=1 m/s的恒定速度向左运动,选手要能到达传送带右端,他从高台上跃出的水平速度v1至少多大?在此情况下到达B点时速度大小是多少?
(1)6.0 s (2)4.08 m/s ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214220095543.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214220095543.png)
试题分析:(1)设选手落在传送带前的运动时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214221452251.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214222560308.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214223886288.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214224697356.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214225477612.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214226553696.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214227723690.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242142280821160.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214228753733.png)
(2)设水平跃出速度v1,落到传送带1 s反应时间内向左位移大小为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214229627337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214229627337.png)
然后设向左减速至速度为零又向左发生位移为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214231577386.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214231982707.png)
不从传送带上掉下,平抛水平位移
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214232793880.png)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214233605887.png)
设在此情况下到达B点时速度大小为v,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214234385559.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242142352111156.png)
点评:解决本题的关键分析出选手的运动情况,然后根据平抛运动和运动学公式求解.
![](http://thumb2018.1010pic.com/images/loading.gif)
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