Question

A plane mirror is receding away from an observer at rest with a speed of $5\text{cm/s}$. If the observer can see his image in the mirror, then image recedes away with speed of

• A. $25\text{cm/s}$
• B. $15\text{cm/s}$
• C. $20\text{cm/s}$
• D. $10\text{cm/s}$

Answer 1

The correct option is D $10\text{cm/s}$


Perpendicular to the mirror,
Velocity of the object $w.r.t$ mirror $=-$ Velocity of the image $w.r.t$ to mirror
$\Rightarrow v_{om}=-v_{im}$
$\Rightarrow v_o-v_m=-(v_i-v_m)$
$\Rightarrow 0-5=-(v_i-5)$
$[$ taking rightward as $+$ $]$
$\Rightarrow v_i=10\text{cm/s}$
Image recedes away at speed of $10\text{cm/s}$.