Velocity of the Image in an Inclined Mirror

When a boy is walking under an inclined mirror at a constant velocity V m/s along the X axis, the mirror reflects the image of the boy. To determine the velocity of the image, we need to consider the angle of inclination (θ) of the mirror with the horizontal.

1. Relative Velocity
The velocity of the image can be found by considering the relative velocity between the boy and the image. Since the boy is moving at a constant velocity V m/s along the X axis, the image will also move in the same direction with the same velocity. Therefore, the velocity of the image is also V m/s along the X axis.

2. Magnitude of the Velocity
The magnitude of the velocity of the image remains the same as the magnitude of the boy's velocity. This is because the image is formed by the reflection of light rays, and the reflection process does not alter the magnitudes of velocities.

3. Direction of the Velocity
The direction of the velocity of the image is determined by the angle of inclination (θ) of the mirror. Let's consider two cases:

a. Horizontal Mirror (θ = 0°)
If the mirror is horizontal (θ = 0°), the image will also move horizontally in the same direction as the boy. Therefore, the velocity of the image will be in the positive X direction.

b. Inclined Mirror (θ ≠ 0°)
If the mirror is inclined at an angle θ with the horizontal, the image will move along a path that is inclined with respect to the X axis. The direction of the image's velocity will depend on the sign of θ:

- If θ is positive, the image will move upwards and to the right.
- If θ is negative, the image will move downwards and to the left.

Summary:
In summary, the velocity of the image will have the same magnitude as the boy's velocity and will move in the same direction as the boy along the X axis. The only difference will be the inclination of the image's path, which depends on the angle of inclination (θ) of the mirror.