A man is 2m50cm standing in front of a vertical mirror at a distance of 3cm,if the mirror is rotated from is initial velocity through and angle of 50degree?

1.determine the size of the image of the man?
2.how far from the man is the image?
3.what is the shortest length of the mirror that will enable the man see himself?
4.when the mirror as been rotated what is the reflected angle?

To calculate the answers to these questions, we can use the principles of mirror reflection and basic trigonometry.

1. To determine the size of the image of the man, we need to use the concept of similarity of triangles. Since the mirror is vertical, the height of the man's image will be the same as the height of the man himself. So, the size of the image is 2m50cm.

2. To find the distance from the man to the image, we need to consider the concept of lateral inversion (left and right reversal in a mirror). The distance between the man and his image is twice the distance between the man and the mirror. In this case, the distance between the man and the mirror is 3cm, so the distance between the man and his image is 2 * 3cm = 6cm.

3. To determine the shortest length of the mirror that will enable the man to see himself, we need to consider the concept of the angle of reflection being equal to the angle of incidence. In this case, the man is standing in front of the mirror, so the angle of incidence is 90 degrees. To calculate the shortest length of the mirror, we need to find the hypotenuse of the triangle formed by the mirror and the man's line of sight. We can use trigonometry to calculate this. The formula to find the hypotenuse (c) is c = d / sin(θ), where d is the distance between the man and the mirror, and θ is the angle of incidence. Substituting the given values, we have c = 3cm / sin(90 degrees) = 3cm.

4. When the mirror as been rotated, the angle of incidence and angle of reflection will change. The reflected angle will be equal to the angle at which the mirror is rotated. In this case, the mirror is rotated at an angle of 50 degrees, so the reflected angle will also be 50 degrees.