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A man of mass m is standing on a platfor...

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

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Consider the situation shown in ure . 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 tehplatform is V+w. By the question
`V+w=v, or w=v-V`........i

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