题目内容
(15分)倾斜雪道的长为25 m,顶端高为15 m,下端经过一小段圆弧过渡后与很长的水平雪道相接,如图所示。一滑雪运动员在倾斜雪道的顶端以水平速度
="8" m/s飞出,在落到倾斜雪道上时,运动员靠改变姿势进行缓冲使自己只保留沿斜面的分速度而不弹起。除缓冲过程外运动员可视为质点,过渡圆弧光滑,其长度可忽略。设滑雪板与雪道的动摩擦因数μ=0.2,求运动员在水平雪道上滑行的距离(取g="10" m/
)。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220583412813.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058325205.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058341199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220583412813.jpg)
s2=74.8 m
如图选坐标,斜面的方程为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220583723101.jpg)
①
运动员飞出后做平抛运动
②
③
联立①②③式,得飞行时间
t=1.2 s
落点的x坐标:x1=v0t=9.6 m
落点离斜面顶端的距离:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058544581.gif)
落点距地面的高度:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058559662.gif)
接触斜面前的x分速度:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058575440.gif)
y分速度:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058591520.gif)
沿斜面的速度大小为:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058606796.gif)
设运动员在水平雪道上运动的距离为s2,由功能关系得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220586221089.gif)
解得:s2=74.8 m
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220583723101.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058388575.gif)
运动员飞出后做平抛运动
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058403364.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058419466.gif)
联立①②③式,得飞行时间
t=1.2 s
落点的x坐标:x1=v0t=9.6 m
落点离斜面顶端的距离:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058544581.gif)
落点距地面的高度:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058559662.gif)
接触斜面前的x分速度:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058575440.gif)
y分速度:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058591520.gif)
沿斜面的速度大小为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058606796.gif)
设运动员在水平雪道上运动的距离为s2,由功能关系得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220586221089.gif)
解得:s2=74.8 m
![](http://thumb2018.1010pic.com/images/loading.gif)
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