Question

A man runs towards a mirror at a speed $+6\text{m/s}$. If the mirror is at rest, his image will have a velocity (with respect to man)

• A. $12\text{m/s}$
• B. $-6\text{m/s}$
• C. $6\text{m/s}$
• D. $-12\text{m/s}$

Answer 1

The correct option is D $-12\text{m/s}$


Given that, man velocity $\left(u\right)=6\text{m/s}$
For a plane mirror,
Object distance = image distance
$\Rightarrow x=x^{\prime }$
Differentiating both sides w.r.t. time,
$\Rightarrow \frac{dx}{dt}=\frac{d{x}^{\prime }}{dt}$
$\Rightarrow u=u^{\prime }=6\text{m/s}$
So, object speed = image speed = $6\text{m/s}$
Taking rightwards as $+ve$ direction,
velocity of image w.r.t. man is $\left(v_{i,m}\right)$
$\Rightarrow v_{i,m}=(-u^{\prime })-u=-2u=-12\text{m/s}$
Hence, option $\left(d\right)$ is the correct answer.