Question

A man run towards the plane mirror at $2m{s}^{-1}$. The relative speed of his image with respect to him will be

• A. $2m{s}^{-1}$
• B. $4m{s}^{-1}$
• C. $18m{s}^{-1}$
• D. $10m{s}^{-1}$

Answer 1

The correct option is B $4m{s}^{-1}$

$\begin{array}{c}\text{we know that sum of}\\ \text{velocity of man with respect to mirror and velocity of}\\ \text{man's image with respect to mirror is zero}\end{array}$

$\Rightarrow V_0-V_m+V_0-V_m=0{\text{Vo}}_1\to \text{velocity of image}$

$\begin{array}{c}{v}_0\to \text{velocity of object}\\ v_m{-}_{\text{velocity}}\text{of mirror}\end{array}$

$\begin{array}{cc}\text{given}& v_0=2m{\overline{s}}^{-1}{v}_m=0\\ & \Rightarrow v_i=-2\end{array}$ velocity of image in the respect to man is

$\begin{array}{cc}v& =V_q-v_0\\ & =-2-2\\ & =-4m/s\\ \text{speed}& =4m/s\end{array}$