Question

A person approaches a plane mirror with velocity V then relative velocity of approach of person and his image is,

Answer 1

the velocity of both will be same

Answer 2

Given:

A person approaches a plane mirror with velocity V.

To find:

Relative velocity of approach of person and his image.

Calculation:

Let's assume that person is approaching the mirror along + x axis ;

So, his Velocity can be represented as :

$\rm{ \vec{v}_{o} = v \: \hat{i}}$

Since , the magnitude of Velocity of image formed by plane mirror will be same (but in opposite direction) , the velocity of image will be :

$\rm{ \vec{v}_{i} = v \: ( - \hat{i})}$

So, Velocity of approach will be :

$\therefore \: \rm{\vec{v}_{o} - \vec{v}_{i} = v \hat{i} - \{ v( - \hat{i}) \}}$

$= > \: \rm{\vec{v}_{o} - \vec{v}_{i} = v \hat{i} - \{ - v \hat{i} \}}$

$= > \: \rm{\vec{v}_{o} - \vec{v}_{i} = v \hat{i} + v \hat{i}}$

$= > \: \rm{\vec{v}_{o} - \vec{v}_{i} = 2v \hat{i} }$

So, Velocity of Approach is :

$\boxed{ \bf{ \red{ \large{\vec{v}_{o} - \vec{v}_{i} = 2v \hat{i}}}}}$