Question

$O$ is the point object shown in the diagram.

If the mirror starts moving with velocity $\sqrt{3} \,m / s$, then find velocity (in $m / s$ ) of the image.

Answer 1

Let the angle of incidence be $\theta$.
Velocity of object, $v_{0}=0$
Velocity of mirror, $v_{m}=-v_{i}$
Velocity of object w.r.t. mirror,
$v_{ om }=v_{o}-v_{m}=+v \hat{i}$
Velocity of image w.r.t mirror,
$v_{l m}=v_{I}-v_{m} $
or, $ v_{I}=v_{l m}+v_{m} $
$v_{l m}=-v \cos 2 \theta \hat{i}-v \sin 2 \theta \hat{j} $
$v_{I}=(-v \cos 2 \theta-v) \hat{i}-v \sin 2 \theta \hat{j}$
Given: $\theta=30^{\circ}, v=\sqrt{3} \,m / s$
$\left|v_{I}\right|=3\, m / s$