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(C) Let the velocity of the object be $\vec{v}_O = v \cos 	heta \hat{i} - v \sin 	heta \hat{j}$,where the $x$-axis is normal to the mirror and the $

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$2v \cos 	heta$

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(C) Let the velocity of the object be $\vec{v}_O = v \cos 	heta \hat{i} - v \sin 	heta \hat{j}$,where the $x$-axis is normal to the mirror and the $y$-axis is parallel to the mirror surface.The image $I$ of an object $O$ formed by a plane mirror has a velocity $\vec{v}_I = -v \cos 	heta \hat{i} - v \sin 	heta \hat{j}$.The relative velocity of the object with respect to the image is $\vec{v}_{OI} = \vec{v}_O - \vec{v}_I$.$\vec{v}_{OI} = (v \cos 	heta \hat{i} - v \sin 	heta \hat{j}) - (-v \cos 	heta \hat{i} - v \sin 	heta \hat{j})$$\vec{v}_{OI} = 2v \cos 	heta \hat{i}$.The magnitude of the relative velocity is $|\vec{v}_{OI}| = 2v \cos 	heta$.

If an object moves towards a plane mirror with a speed $v$ at an angle $\theta$ to the normal of the plane of the mirror,find the relative velocity between the object and the image.

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