Figure shows the system is at rest initially with `x = 0`, A man and a woman both are initially at the extreme carrier of the platform. The man and the woman start to move towards each other. Obtain an expression for the displacement `s` of the platform when the two meet in terms of the displacement `x_1` of the man relative to the platform. `

Explanation

As no external force is acting on the system the diplacemnte of the centre of mass should be zero.
Let the displacement of the platform toward right be `s`.
`/_\vecx_(1)=/_\vecx_(1,p)+/_\vecv_(p)=(-x_(1)+s)`
`/_\vecx_(2)=/_\vecx_(2,p)+/_\vecx_(p)=(l-x_(1)+s)`
Hence,
`0=(m_(1)(-x_(1)+s)+m_(2)(l-x_(1)+s)+m_(0)s)/(m_(1)+m_(2)+m_(3))`
`s(m_(1)+m_(2)+m_(0))-m_(1)x_(1)+m_(2)(l-x_(1))=0`
`s=(m_(1)x_(1)-m_(2)(l-x_(1)))/(m_(1)+m_(2)+m_(0))`