Question

An observer runs towards a plane mirror with a velocity x m/s. What
is the velocity of his image which will appear to move towards him?​

Answer 1

Given:

An observer runs towards a plane mirror with a velocity x m/s.

To find:

The velocity of his image which will appear to move towards him?

Calculation:

Refer to attached diagram for understanding the coordinate axes.

Now , velocity of the man be v_(o) :

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

Now , the image of the man moves with a velocity of v_(i) :

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

$\implies \: \vec{v}_{i} = - x \hat{i}$

So, velocity of image as seen by man :

$\therefore \: \vec{v}_{io} = \vec{v_{i}} - \vec{v_{o}}$

$\implies \: \vec{v}_{io} = - x \hat{i} - (x \hat{i})$

$\implies \: \vec{v}_{io} = - 2x \hat{i}$

$\implies \: \vec{v}_{io} = 2x( - \hat{i} )$

So, required answer is :

$\boxed{ \bold{\: \vec{v}_{io} = 2x( - \hat{i} )}}$