Question

An object $O$ is moving with velocity $(\hat{i}+2\hat{j}+3\hat{k})\text{m/s}$ and a plane mirror facing the object is lying in $(y-z)$ plane. If the mirror is moving with velocity $2\hat{i}\text{m/s}$, the velocity of image w.r.t object (in SI units) is :

• A. $-\hat{i}+2\hat{j}+3\hat{k}$
• B. $2\hat{i}$
• C. $3\hat{i}+2\hat{j}+\hat{k}$
• D. $-\hat{i}-2\hat{j}-3\hat{k}$

Answer 1

The correct option is B $2\hat{i}$

For the mirror lying in $(y-z)$ plane, the $x$-axis will represent the normal direction for the mirror.

Therefore, along the normal to mirror :
$(v_m{)}_x=\frac{(v_o{)}_x+(v_i{)}_x}{2}$
$\Rightarrow 2\hat{i}=\frac{1\hat{i}+(v_i{)}_x}{2}$
$\therefore (v_i{)}_x=(4-1)\hat{i}=3\hat{i}\text{m/s}$

Mirror is lying along $(y-z)$ plane, therefore $(v_i{)}_y$ and $(v_i{)}_z$ will be same as that of object velocity component
$\Rightarrow (v_i{)}_y=2\hat{j},(v_i{)}_z=3\hat{k}$
or, ${\overrightarrow{v}}_i=(3\hat{i}+2\hat{j}+3\hat{k})\text{m/s}$

Velocity of image w.r.t object,
${\overrightarrow{v}}_{i,o}=(3\hat{i}+2\hat{j}+3\hat{k})-(\hat{i}+2\hat{j}+3\hat{k})$
$\therefore {\overrightarrow{v}}_{i,o}=2\hat{i}\text{m/s}$