Q. A man moves towards a plane mirror with a velocity $v$ in a direction making an angle $\text{\theta }$ with the normal to the mirror. Find out the magnitude of the velocity of the image relative to normal to mirror.

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A

$2v$

B

$2vcos\text{\theta }$

C

$2vsin\text{\theta }$

D

$\frac{2 v}{C o s \text{\theta }}$

Solution:

The velocity of the man perpendicular to the mirror is given as Vcosθ
The image also approaches with the same velocity towards the man.
Thus the relative velocity is given as Vcosθ−(−Vcosθ)=2Vcosθ.

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