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Question

A plane mirror is placed along the y - axis such that the x - axis is normal to the plane of the mirror. The reflecting surface of the mirror is towards the negative x - axis. The mirror moves in positive x - direction with uniform speed of 5 m/s and a point object P is moving with constant speed of 3 m/s in negative x - direction. The speed of the image with respect to the mirror will be

A
8 m/s
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B
2 m/s
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C
4 m/s
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D
6 m/s
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Solution

The correct option is A 8 m/s
According to the question, the below diagram represents the object and mirror velocity.

Along perpendicular to the mirror,
Velocity of the object w.r.t mirror = Velocity of the image w.r.t to mirror
vom=vim
vovm=(vivm)
(3)5=(vi5)
[ taking rightward as + ]
vi=13 m/s
[ with respect to ground ]
Now, speed of the image with respect to the mirror,
vim=vivm=135=8 m/s
[ taking rightward as + ]

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