Two plane mirrors are placed as shown in figure. A point object $O$ is approaching the intersection point $A$ of mirrors with a speed of $100cm/s$. The velocity of image of the object formed by $M_2$ with respect to velocity of image of object formed by $M_1$ is:-

The correct option is A $-128\hat{i}+96\hat{j}cm/s$
$\begin{array}{c}Velocityofimageformby{M}_1=100cm/s\hat{i}\\ \Rightarrow {\overrightarrow{V}}_1=100cm/s\hat{i}\\ Velocityofimageformedby{M}_2=-100\cos \left(2\times {37}^0\right)\hat{i}+100\sin \left(2\times {37}^0\right)\hat{j}\\ =-100\left[1-2\times \frac{9}{25}\right]\hat{i}+100\left(2\times \frac{3}{5}\times \frac{4}{5}\right)\hat{j}\\ =\frac{-100\times 7}{25}\hat{i}+\frac{100\times 24}{25}\hat{j}\\ =-28\hat{i}+96\hat{j}\\ \therefore relativevelocity={\overrightarrow{V}}_2-{\overrightarrow{V}}_1\\ =-128\hat{i}+96\hat{j}cm/s\\ Hence,\\ optionAiscorrectanswer.\end{array}$