22.
(2021高一上·宁波期末)
如图所示为某物理兴趣小组所设计的游戏装置示意图。质量
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmtext%3Ek%3C%2Fmtext%3E%3Cmtext%3Eg%3C%2Fmtext%3E%3C%2Fmath%3E)
的小钢珠(视为质点)用长度
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EL%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
的轻绳拴着在竖直面内绕O做圆周运动。钢珠在A处轻绳恰好断开,以
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ev%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmtext%3E%2F%3C%2Fmtext%3E%3Cmtext%3Es%3C%2Fmtext%3E%3C%2Fmath%3E)
的速度水平抛出,不计空气阻力,钢珠飞出后恰好从B处无碰撞切入一倾角为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%CE%B8%3C%2Fmtext%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmath%3E)
的斜面上,从C处小圆弧以2m/s的速度水平抛出,已知抛出点距地面高为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Eh%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
, 钢珠在抛出后将与地面发生弹性碰撞,碰撞前后速度水平分量不变,速度的竖直分量大小不变,方向相反,若钢珠在第一次碰撞前恰好掠过高为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Eh%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
的挡板D,之后经过一次碰撞又恰好掠过高为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Eh%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
的挡板E,最后打中位于F处的电灯开关(开关大小不计,可视为点)。求:
![](//tikupic.21cnjy.com/2022/03/03/37/d5/37d570019c7fa34adc52925758fee339_430x272.png)