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

Answer: 3

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,
$v_{lm}=v_I-v_m$
or, $v_I=v_{lm}+v_m$
$v_{lm}=-v\cos 2\theta \hat{i}-v\sin 2\theta \hat{j}$
$v_I=(-v\cos 2\theta -v)\hat{i}-v\sin 2\theta \hat{j}$
Given: $\theta =30^{\circ },v=\sqrt{3}m/s$
$\left|v_I\right|=3m/s$