Question

According to a stationary observer on ground, a point object $O$ in front of a plane mirror $M$ and the mirror both are moving at $10\text{cm/s}$ and $20\text{cm/s}$ respectively towards right. Find the speed of the image as measured by the stationary observer.

• A. $10\text{cm/s}$
• B. $5\text{cm/s}$
• C. $20\text{cm/s}$
• D. $30\text{cm/s}$

Answer 1

The correct option is D $30\text{cm/s}$

${\overrightarrow{x}}_{IM}={\overrightarrow{x}}_{MO}$
${\overrightarrow{x}}_{IG}-{\overrightarrow{x}}_{MG}={\overrightarrow{x}}_{MG}-{\overrightarrow{x}}_{OG}$
$\Rightarrow {\overrightarrow{v}}_{IG}-{\overrightarrow{v}}_{MG}={\overrightarrow{v}}_{MG}-{\overrightarrow{v}}_{OG}$
$\Rightarrow {\overrightarrow{v}}_{IG}=2{\overrightarrow{v}}_{MG}-{\overrightarrow{v}}_{OG}$
$\Rightarrow {\overrightarrow{v}}_{IG}=2\left(20\text{cm/s}\right)-10\text{cm/s}=30\text{cm/s}$