Question

An object is moving with a velocity of $2\hat{i}+3\hat{j}+6\hat{k}$. A plane mirror whose reflecting surface is parallel to $y-z$ plane is moving with a velocity of $\hat{i}+\hat{j}+\hat{k}$. What is the velocity of the image as seen by a stationary observer?

• A. $\hat{j}+4\hat{k}$
• B. $3\hat{j}+6\hat{k}$
• C. $-\hat{j}-4\hat{k}$
• D. $-\hat{i}+3\hat{j}+6\hat{k}$

Answer 1

The correct option is B $3\hat{j}+6\hat{k}$

In the direction perpendicular to mirror $(\hat{i}$),
$V_{Ix}-V_{Mx}=-[V_{Ox}-V_{Mx}]$
$\Rightarrow V_{Ix}=2V_{Mx}-V_{Ox}=2\times 1\hat{i}-2\hat{i}=0$

In the direction parallel to mirror,
$V_{Iyz}=V_{Oyz}=3\hat{j}+6\hat{k}$

Hence, velocity of image seen by a stationary oberver
$V_I=3\hat{j}+6\hat{k}$