(A) The velocity of the object is given by $\vec{v}_{obj} = 3\hat{i} + 4\hat{j}$.Since the mirror is placed along the $x$-axis,the $x$-component of th

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(A) The velocity of the object is given by $\vec{v}_{obj} = 3\hat{i} + 4\hat{j}$.Since the mirror is placed along the $x$-axis,the $x$-component of the velocity remains unchanged for the image,while the $y$-component (perpendicular to the mirror) is reversed.Therefore,the velocity of the image is $\vec{v}_{im} = 3\hat{i} - 4\hat{j}$.The relative velocity of the image with respect to the object is $\vec{v}_{rel} = \vec{v}_{im} - \vec{v}_{obj}$.Substituting the values: $\vec{v}_{rel} = (3\hat{i} - 4\hat{j}) - (3\hat{i} + 4\hat{j}) = 3\hat{i} - 4\hat{j} - 3\hat{i} - 4\hat{j} = -8\hat{j}$.

Class 12 Physics Ray Optics and Optical Instruments Velocity in Mirrors (Kinematics)

Medium

$A$ plane mirror is placed along the $x$-axis facing the negative $y$-axis. The mirror is fixed. $A$ point object is moving with a velocity of $3\hat{i} + 4\hat{j}$ in front of the plane mirror. Find the relative velocity of the image with respect to the object.

A
$-8\hat{j}$
B
$8\hat{j}$
C
$3\hat{i} - 4\hat{j}$
D
$-6\hat{i}$

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Ray Optics and Optical Instruments

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Velocity in Mirrors (Kinematics)

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$A$ plane mirror is placed along the $x$-axis facing the negative $y$-axis. The mirror is fixed. $A$ point object is moving with a velocity of $3\hat{i} + 4\hat{j}$ in front of the plane mirror. Find the relative velocity of the image with respect to the object.

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