A man of maas m is standing on a platform of maas M kept on smooth ice. If the man starts moving on the platform with a speed v relative to the platform with what velcity relative to the ice does the platform recoil?

Explanation

Consider the situation shown in figure. Suppose the man moves at a speed w towards right and the platform recoils at a speed V towards left, both relative to the ice. Hence, the speed of the man relative to the platform is `V + w`. By the question, `V + w = v, or w = v – V " "`........(i)

Taking the platform and the man to be the system, there is no external horizontal force on the system. The linear momentum of the system remains constant. Initially both the man and the platform were at rest. Thus,
`0=MV-mw`
or, `MV=m(v-V)`[Using (i)]
or, `V=(mv)/(M+m)`.