某次交警勘查车祸现场,技术人员需要根据现场情况估算碰撞前的车速情况,已知该事故发生在平坦路段,人车碰撞后瞬间车开始完全制动,事故发生的示意图如图所示,车辆质量为M,行人质量为m,车辆与地面间的动摩擦因数为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3E%CE%BC%3C%2Fmi%3E%3C%2Fmath%3E)
,重力加速度为g,忽略碰撞前人的速度,不考虑空气阻力的影响。现有两种碰撞车速v的估算模型,其一为基于车辆制动距离
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3ES%3C%2Fmi%3E%3Cmtext%3Ev%3C%2Fmtext%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的碰撞车速估算(
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3ES%3C%2Fmi%3E%3Cmtext%3Ev%3C%2Fmtext%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
为碰撞结束后车辆滑行的距离),该模型特点:碰撞时间极短,碰后车、人快速达到共同速度;其二为基于行人抛距
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3ES%3C%2Fmi%3E%3Cmtext%3Ep%3C%2Fmtext%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的碰撞车速估算,该模型特点:碰撞时间极短,行人被撞飞的速度等于碰后瞬间车辆速度,行人被水平撞飞,行人与地面撞击后,没有反弹而是在地面滑行,人与地面间的动摩擦因数为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmi%3E%CE%BC%3C%2Fmi%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
,R为行人从碰撞结束时刻的位置至第一落地点之间沿道路的距离;h为行人被撞飞时的重心高度;S为行人落地后滑行的距离;
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3ES%3C%2Fmi%3E%3Cmtext%3Ep%3C%2Fmtext%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3ES%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
为行人抛距。求: