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Q. A point object is moving with velocity $6 \hat{i}+\hat{j}+2 \hat{k}$ $( m / s )$ in front of a plane mirror whose reflecting side is $x z$-plane. If the mirror also moves with a velocity $\hat{i}-\hat{j}$ $( m / s )$, then what is the speed (in $m / s$ ) of the image? (Round-off the answer to nearest integer)

Ray Optics and Optical Instruments

Solution:

image
$=6 \hat{i}-3 \hat{j}+2 \hat{k} $
$ v_{I} =\sqrt{36+9+4}=\sqrt{49}=7 \,m / s $