A big plane mirror is fixed vertically on the back of bicyce. A boy standing in front of the

mirror can see his image clearly in the plane mirror. The bicycle starts moving with the
sepeed of 6 ms–1 and the boy also starts running with 4 ms–1 in the direction of bicycle
motion to keep his image in the plane mirror.
(i) What is the speed of boy with respect to bicycle?
(ii) What is the speed of image in plane mirror with respect to boy.
(iii) Will the size of the image increase, decrease or remain thee same.

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To answer these questions, we need to use the concept of relative velocities.

(i) The speed of the boy with respect to the bicycle can be calculated by subtracting the bicycle's speed from the boy's speed. In this case, the boy is running at a speed of 4 m/s, and the bicycle is moving at a speed of 6 m/s. Therefore, the speed of the boy with respect to the bicycle is 4 m/s - 6 m/s = -2 m/s. The negative sign indicates that the boy is moving in the opposite direction to the bicycle.

(ii) The speed of the image in the plane mirror with respect to the boy can be found by considering that the image appears to move at twice the speed of the object it is reflecting. Since the boy is running with a speed of 4 m/s, the speed of the image in the mirror with respect to the boy will be twice that, which is 8 m/s.

(iii) The size of the image in the plane mirror remains the same regardless of the relative speed and direction of motion. The mirror reflects the light rays from the boy and forms an image that is the same size as the boy. Therefore, the size of the image does not change.

To summarize:
(i) The speed of the boy with respect to the bicycle is -2 m/s. (-2 m/s indicates that the boy is moving in the opposite direction to the bicycle.)
(ii) The speed of the image in the plane mirror with respect to the boy is 8 m/s.
(iii) The size of the image in the plane mirror remains the same.