Question

If an object moves toward a plane mirror with a speed $v$ at an angle $\theta$ with respect to the perpendicular to the plane of
the mirror, find the relative velocity of the object w.r.t. image.

Answer 1

Velocity of the objective relative to the image is given as
${\overrightarrow{v}}_D={\overrightarrow{v}}_O-{\overrightarrow{v}}_1$
${\overrightarrow{v}}_{Ol}=(v\cos \theta \hat{i}-v\sin \theta \hat{j})+(v\cos \theta \hat{i}+v\sin \theta \hat{j})$
$\Rightarrow {\overrightarrow{v}}_D=2v\cos \theta \hat{i}$
$\Rightarrow v_{Ol}=2v\cos \theta$