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/sAccording 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 ⇒→vo−→vm=−(→vi−→vm) ⇒(−3)−5=−(→vi−5) [ taking rightward as + ] ⇒→vi=13 m/s [ with respect to ground ] Now, speed of the image with respect to the mirror, →vim=→vi−→vm=13−5=8 m/s [ taking rightward as + ]

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