An observer moves towards a stationary plane mirror at a speed of 4 ms${}^{-1}$. What is the relative speed of the image with respect to the observer?

The correct option is C 8 ms${}^{-1}$

velocity of object with respect to mirror, $v_{o,m}=-4m/s=\frac{-dx}{dt}$ taking right direction as positive .

velocity of image with respect to mirrot, $v_{i,m}=\frac{d{x}^{{}^{\prime }}}{dt}=\frac{dx}{dt}=4m/s$ since $x^{{}^{\prime }}=x$

Now, $v_{i,o}=v_{i,m}+v_{m,o}=v_{i,m}-v_{o,m}$

$⟹v_{i,o}=4-(-4)=8m/s$

Answer-(C)