(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)

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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.

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

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Velocity in Mirrors (Kinematics)

$A$ plane mirror is moving with velocity $4\hat i + 5\hat j + 8\hat k$. $A$ point object in front of the mirror moves with a velocity $3\hat i + 4\hat j + 5\hat k$. Here,the $\hat k$ direction is along the normal to the plane mirror and facing towards the object. The velocity of the image is:

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$A$ point object on the principal axis at a distance $1.5\, cm$ in front of a concave mirror of radius of curvature $20\, cm$ has velocity $2\, mm/s$ perpendicular to the principal axis. The velocity of image at that instant will be.....$mm/s$

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An object is at a distance of $20\,m$ from a convex lens of focal length $0.3\,m$. The lens forms an image of the object. If the object moves away from the lens at a speed of $5\,m/s$,the speed and direction of the image will be

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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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$A$ plane mirror is moving with velocity $4\hat i + 5\hat j + 8\hat k$. $A$ point object in front of the mirror moves with a velocity $3\hat i + 4\hat j + 5\hat k$. Here,the $\hat k$ direction is along the normal to the plane mirror and facing towards the object. The velocity of the image is:

An object is moving with a velocity of $2 \ m/s$ to the left,and a plane mirror is moving with a velocity of $9 \ m/s$ to the right. Find the velocity of the image with respect to the ground.

$A$ car is fitted with a convex side-view mirror of focal length $20\ cm$. $A$ second car $2.8\ m$ behind the first car is overtaking the first car at a relative speed of $15\ m/s$. The speed of the image of the second car as seen in the mirror of the first one is

$A$ point object on the principal axis at a distance $1.5\, cm$ in front of a concave mirror of radius of curvature $20\, cm$ has velocity $2\, mm/s$ perpendicular to the principal axis. The velocity of image at that instant will be.....$mm/s$

An object is at a distance of $20\,m$ from a convex lens of focal length $0.3\,m$. The lens forms an image of the object. If the object moves away from the lens at a speed of $5\,m/s$,the speed and direction of the image will be

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