A man 100 kg is standing on a platform of mass 200 kg which is kept on ice surface.If the man starts moving with speed 30m/s relative to the platform then,find what velicity relative to ice the platform will recoil ??

Am I to assume that there is no friction between ice surface and platform?
as it is not stated, we assume that way



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Momentum of the man + platform is a constant  and is 0.  Reason is that there is no net external force acting on this system.  Hence as per Newton's 2nd law, the momentum is conserved.

We take the velocities wrt to ice (static/inertial reference).  Let velocity of the recoil of the platform be V m/s.  Then the man is moving wrt the ice  in the opposite direction at (30-V) velocity.

           100 * (30-V) - 200 * V = 0
            300 V = 3000

Recoil velocity V = 10 m/s  in the opposite direction of movement of the man.
Velocity of the man wrt to ice = 20m/s
 (Their relative velocity = 30 m/s)

2 4 2
Okay then
the answer is 10 m/s
when i do the problem with cm
what do u mean ?
i solved the sum with center of mass