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A sphere of mass m is ropped from a height h above the ground. on reaching theground it penetrates through a distance S and finally stops. the average resistance offered bythe sand to oppose the motion is
At height h it has a initial speed u=0.Just before hitting the ground its speed v isv2=u2+2fs=2ghor,v=root(2gh)So it hits the ground with an initial speed u=root(2gh) and after covering a distance s it comes to rest,ie,its final velocity v=0.If f is its acceleration inside ground thenv2=u2+2fsOr,0=2gh+2fsOr,f=-gh/sSo the resistance(force) offered by sand ismf=mgh/sHope this helps
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