# "When you both stop, I stop" - Centre Of Mass

Two particles $$A$$ and $$B$$ are situated on a horizontal table top of infinite surface area whose surface is considered as the $$x-y$$ plane. The mass of $$A$$ is $$1~kg$$ and that of $$B$$ is $$2~kg$$. At time $$t=0$$, particle $$A$$ is at $$(3,0)$$ and particle $$B$$ is at $$(0,9)$$. Both particles are given initial velocites:

• $$3~ms^{-1}$$ to $$A$$ along positive $$x$$-axis and

• $$6~ms^{-1}$$ to $$B$$ along positive $$y$$-axis.

If the coefficient of friction between each particle and the table top is $$\mu = 0.2$$ & the coordinates of the position of the centre of mass of $$A$$ and $$B$$, where it comes to rest can be expressed as $$\left(\dfrac{a}{b},\dfrac{c}{d}\right)$$, where $$\left\{a,b\right\}$$ and $$\left\{c,d\right\}$$ are pairwise co-prime positive integers, then enter your answer as

$$\displaystyle (c+d)-(a+b)$$.

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