Question

A plane mirror is placed parallel to y-axis with its center at origin $(0,0,0)$. An object starts the motion in front of the mirror from position $(2,0)\text{m}$ with a velocity $(2\hat{i}+2\hat{j})\text{m/s}$. The relative velocity of image with respect to the object is along

• A. positive x-axis
• B. positive y-axis
• C. negative y-axis
• D. negative x-axis

Answer 1

The correct option is D negative x-axis

Applying ${\overrightarrow{v_o}}_{\perp }=-({\overrightarrow{v}}_i{)}_{\perp }$, we get the velocity of object and image as shown in above diagram.
$\Rightarrow {\overrightarrow{v}}_{i,o}={\overrightarrow{v}}_i-{\overrightarrow{v}}_o$
or, ${\overrightarrow{v}}_{i,o}=(-2\hat{i}+2\hat{j})-(2\hat{i}+2\hat{j})$
$\therefore {\overrightarrow{v}}_{i,o}=-4\hat{i}\text{m/s}$
Relative velocity of image w.r.t object is along negative x-axis.