A man of mass `m_(1)` stands at an edge `A` of a plank of mass `m_(2)` & length `l` which is kept on a smooth floor If man walks from `A` to the other edge `B` find displacement of plank.

Explanation

Let the displacement of the plank be `s_(2)`
Initial momentum of system (man and plank) is zero.
Net external force on this system is zero.
Thus during the course of motionvec`vecP_("sys")=0rArrvec"v"_("cm")=0rArr vec"s"_("cm")=0`
`rArr" "m_(1)vecs_(1)+m_(2)vecs_(2)=0`
`m_(1)vecs_(1)=-m_(2)vecs_(2)`
in scalar form
`m_(1)|vecs_(1)|=m_(2)|vecs_(2)|`
`m_(1)(l-s_(2))=m_(2)s_(2)`
`s_(2)=(m_(1)l)/(m_(1)+m_(2))`
The plank moves backward because as the man moves forward, he pushes on the plank backwards.