A plane mirror and an object approach each other with speeds of 5 ms−1 and 10 ms−1 respectively. What will be the speed of the image w.r.t. the stationary observer?
Speed of object, uo=5 ms−1
Speed of mirror, um=10 ms−1
Mirror and object are approaching each other.
Speed of image
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:
Position of mirror will be:
Let the final position of image be xif
Using object distance equals image distance after time t.
Distance moved by image in time t is:
Speed is the ratio of distance and time. Speed of the image is:
Negative sign appears because image is moving leftwards.
Hence, speed of image is 25 ms−1