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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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The correct Answer is:
A, B
Absolute velocity of man `=v_r-v` where v=recoil velocity of platform.

Taking the platform and the man as a system, net external force on the system in horizontal direction is zero. The linear momentum of the system remains constant. Initially both the man and the platform were at rest.
Hence, `0=m_1(v_r-v)-m_2v`
`:. v=(m_1v_r)/(m_1+m_2)`
Alternate Method Using the equation,
`summ_Rv_R=summ_Lv_L`
we have, `m_1(v_r-v)=m_2v`
`:. v=(m_1v_r)/(m_1+m_2)`
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