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Question

A plane mirror and an object approach each other with speeds of 5 ms1 and 10 ms1 respectively. What will be the speed of the image w.r.t. the stationary observer?


A

5 ms1

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B

15 ms1

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C

20 ms1

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D

25 ms1

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Solution

The correct option is D

25 ms1


Given:
Speed of object, uo=5 ms1
Speed of mirror, um=10 ms1
Mirror and object are approaching each other.

To find:
Speed of image

Procedure:
Let initial position of object be at xoi=0
Let initial position of mirror be at xmi=u
Object distance equals the image distance. Hence, initial position of image is xii=2u

Distance is the product of speed and time.
After time t,
Position of object will be:
xof=xoi+uot=5t
Position of mirror will be:
xmf=xmiuft=u10t

Let the final position of image be xif
Using object distance equals image distance after time t.
xifxmf=xmfxof
xif=2u25t

Distance moved by image in time t is:
si=xifxii
si=25t

Speed is the ratio of distance and time. Speed of the image is:
vi=sit=25

Negative sign appears because image is moving leftwards.
Hence, speed of image is 25 ms1


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