• # question_answer A plane mirror is placed at x = 0 with its plane parallel to the y-axis. An object starts from x = 3 m and moves with a velocity of $(2\hat{i}+2\hat{j})m{{s}^{-1}}$ away from the mirror The relative velocity of the image with respect to the object is A) $2\sqrt{2}\,m{{s}^{-1}}$ making an angle of $45{}^\circ$ with the $+x$ axis B) $2\sqrt{2}\,m{{s}^{-1}}$ making an angle of $135{}^\circ$ with the $+x$ axis C) $4\text{ }m{{s}^{-1}}$ along the $-x$ axis D) $4\text{ }m{{s}^{-1}}$ along the $+x$ axis

 Velocity of the object is ${{\overrightarrow{v}}_{_{0}}}=(2\hat{i}+2\hat{j})m{{s}^{-1}}$ $\therefore$Speed of object is ${{v}_{i}}=\sqrt{{{2}^{2}}+{{2}^{2}}}=2\sqrt{2}m{{s}^{-1}}$ =speed of the image$({{v}_{i}})$. The velocity ${{\overrightarrow{v}}_{1}}$of the image will be as shown in fig. the relative velocity of the image with respect to the object is $\Delta \overrightarrow{v}={{\overrightarrow{v }}_{1}}-{{\overrightarrow{v}}_{0}}={{\overrightarrow{v}}_{1}}+(-{{\overrightarrow{v}}_{0}})$ $={{\left[ {{\left( 2\sqrt{2} \right)}^{2}}+{{\left( 2\sqrt{2} \right)}^{2}} \right]}^{1/2}}=4\,m{{s}^{-1}}\,\,along-x\,\,axis.$