2020年11月24日凌晨4时30分,我国在中国文昌航天发射场,用长征五号运载火箭成功发射探月工程嫦娥五号探测器。12月1日23时,嫦娥五号探测器在月面上空开启发动机,实施降落任务。在距月面高为
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EH%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E102%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
m处开始悬停,识别障碍物和坡度,选定相对平坦的区域后,先以a匀加速下降,加速至
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmsqrt%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmsqrt%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
m/s时,立即改变推力,以
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmsup%3E%3Cmtext%3Es%3C%2Fmtext%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
匀减速下降,至月表高度30m处速度减为零,立即开启自主避障程序,缓慢下降。最后距离月面2.5m时关闭发动机,探测器以自由落体的方式降落,整个过程始终垂直月球表面作直线运动,取竖直向下为正方向。已知嫦娥五号探测器的质量
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E40%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
kg,月球表面重力加速度为
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmtext%3E1%3C%2Fmtext%3E%3Cmtext%3E.6m%3C%2Fmtext%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmsup%3E%3Cmtext%3Es%3C%2Fmtext%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
。求:
![](http://tikupic.21cnjy.com/2021/06/24/e38451c77ac2049aa6621c7182fb3d79.png)