Question

A man is walking under an inclined mirror at a constant velocity $Vm{s}^{-1}$ along the $X-axis$. If the mirror is inclined at an angle $\theta$ with the horizontal, then what is the velocity of the image?

• A. $Vsin\theta \hat{i}+V\cos \theta \hat{j}$
• B. $V\cos \theta \hat{i}+V\sin \theta \hat{j}$
• C. $V\sin 2\theta \hat{i}+V\cos 2\theta \hat{j}$
• D. $V\cos 2\theta \hat{i}+V\sin 2\theta \hat{j}$

Answer 1

Answer: (D)

$V\cos 2\theta \hat{i}+V\sin 2\theta \hat{j}$

Component of $V$ perpendicular to the mirror gets reversed while that parallel to it mirror same. Thus, velocity vector of image becomes
$V\cos 2\theta \hat{i}+V\sin 2\theta \hat{j}$.