Question

Two ice-skaters of mass $120\text{kg}$ and $200\text{kg}$ are initially hugging on a frictionless ice surface. Ten seconds after they push off from each other, they are $8.0\text{m}$ apart. The distance moved by the skater of mass $200\text{kg}$ is (in $\text{m}$)

Answer 1

As there is no external force, $COM$ will not change its position. Considering initial point as origin.
Let $x$ be displacement of $120\text{kg}$, then displacement of $200\text{kg}$ is $8-x$
$\Rightarrow 120\left(x\right)=200(8-x)$
$\Rightarrow 1600-320x=0$
$\Rightarrow x=5\text{m}$ (position of $120\text{kg}$)
Displacement of $200\text{kg}$ will be $(8-5)=3\text{m}$