Question

A plane mirror is placed along the $y$ - axis such that the $x$ - axis is normal to the plane of the mirror. The reflecting surface of the mirror is towards the negative $x$ - axis. The mirror moves in positive $x$ - direction with uniform speed of $5\text{m/s}$ and a point object $P$ is moving with constant speed of $3\text{m/s}$ in negative $x$ - direction. The speed of the image with respect to the mirror will be

• A. $8\text{m/s}$
• B. $2\text{m/s}$
• C. $4\text{m/s}$
• D. $6\text{m/s}$

Answer 1

The correct option is A $8\text{m/s}$

According to the question, the below diagram represents the object and mirror velocity.

Along perpendicular to the mirror,
Velocity of the object $w.r.t$ mirror $=-$ Velocity of the image $w.r.t$ to mirror
$\Rightarrow {\overrightarrow{v}}_{om}=-{\overrightarrow{v}}_{im}$
$\Rightarrow {\overrightarrow{v}}_o-{\overrightarrow{v}}_m=-({\overrightarrow{v}}_i-{\overrightarrow{v}}_m)$
$\Rightarrow (-3)-5=-({\overrightarrow{v}}_i-5)$
$[$ taking rightward as $+$ $]$
$\Rightarrow {\overrightarrow{v}}_i=13\text{m/s}$
$[$ with respect to ground $]$
Now, speed of the image with respect to the mirror,
${\overrightarrow{v}}_{im}={\overrightarrow{v}}_i-{\overrightarrow{v}}_m=13-5=8\text{m/s}$
$[$ taking rightward as $+$ $]$