Question

Find the velocity of the image, when the object and mirror are in motion as shown in the figure below.

• A. ${\overrightarrow{v}}_i=-6\hat{i}$
• B. ${\overrightarrow{v}}_i=12\hat{i}$
• C. ${\overrightarrow{v}}_i=3\hat{i}$
• D. ${\overrightarrow{v}}_i=-12\hat{i}$

Answer 1

The correct option is D ${\overrightarrow{v}}_i=-12\hat{i}$

In the direction normal to the mirror,

Relative velocity of image with respect to mirror= Relative velocity of object with respect to mirror

$\text{i.e}{\overrightarrow{v}}_i-{\overrightarrow{v}}_m=-({\overrightarrow{v}}_o-{\overrightarrow{v}}_m)$

$\Rightarrow {\overrightarrow{v}}_i=2{\overrightarrow{v}}_m-{\overrightarrow{v}}_o$

From the data given in the question,

${\overrightarrow{v}}_m=(-\hat{i})\text{m/s},{\overrightarrow{v}}_o=10\hat{i}\text{m/s}$

$\Rightarrow {\overrightarrow{v}}_i=2\times (-\hat{i})-\left(10\hat{i}\right)$

$\Rightarrow {\overrightarrow{v}}_i=-12\hat{i}\text{m/s}$