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.

(i) 10 m/s

(ii) 20 m/s

(iii) Image size will increase, until they collide or pass each other

seems to me that since the mirror is on the back of the bicycle, the boy is chasing the bike, but losing ground at 2m/s.

To answer these questions, we need to understand the concepts of relative velocity and the behavior of images in plane mirrors.

(i) The speed of the boy with respect to the bicycle can be calculated by subtracting the speed of the bicycle from the speed of the boy. In this case, the boy is running with a speed of 4 m/s and the bicycle is moving with a speed of 6 m/s. So, the speed of the boy with respect to the bicycle would be:
Speed of boy with respect to bicycle = Speed of boy - Speed of bicycle
Speed of boy with respect to bicycle = 4 m/s - 6 m/s
Speed of boy with respect to bicycle = -2 m/s (negative because the boy is running in the opposite direction of the bicycle's motion)

(ii) The speed of the image in the plane mirror with respect to the boy can be determined by considering the reflection of light. The speed of light is constant (approximately 3 x 10^8 m/s), and the image in the mirror appears at the same distance behind the mirror as the actual boy is in front of the mirror. Therefore, the speed of the image in the plane mirror with respect to the boy will be the same as the speed of light, which is approximately 3 x 10^8 m/s.

(iii) The size of the image in a plane mirror remains the same regardless of the speed of the objects in front of it. The image formed in a plane mirror is a virtual image, meaning it is formed by the apparent intersection of reflected rays. The size of the image is determined by the distance between the object and the mirror, rather than the speed of the object or the mirror.

To summarize:
(i) The speed of the boy with respect to the bicycle is -2 m/s.
(ii) The speed of the image in the plane mirror with respect to the boy is approximately 3 x 10^8 m/s.
(iii) The size of the image will remain the same.