Two concave mirrors of equal radii of curvature R are fixed on a...

Two concave mirrors of equal radii of curvature $R$ are fixed on a stand facing opposite directions. The whole system has a mass $m$ and is kept on a frictionless horizontal table as shown in the figure. Two blocks $A$ and $B$, each of mass $m$, are placed on the two sides of the stand. At $t = 0$, the separation between $A$ and the mirrors is $2R$ and also the separation between $B$ and the mirrors is $2R$. The block $B$ moves towards the mirror at a speed $v$. All collisions which take place are elastic. Taking the original position of the mirrors–stand system to be $x = 0$ and X-axis along $AB$, find the position of the images of $A$ and $B$ at $t =$ (a) $\dfrac{R}{v}$ (b) $\dfrac{3R}{v}$ (c) $\dfrac{5R}{v}$.