A man approaches a vertical plane mirror at speed of 2 m//s. At what rate does he approach his image?

Explanation

To solve the problem of how fast the man approaches his image in a vertical plane mirror, we can follow these steps:

### Step 1: Understand the scenario
The man is moving towards a vertical plane mirror at a speed of 2 m/s. In a plane mirror, the image of the object (the man) is formed at the same distance behind the mirror as the object is in front of it.

### Step 2: Determine the speed of the image
Since the mirror is a plane mirror, the image will move towards the mirror at the same speed as the man is moving towards the mirror. Therefore, the speed of the image is also 2 m/s.

### Step 3: Calculate the rate of approach to the image
The rate at which the man approaches his image is the sum of the speed of the man and the speed of the image. Since both the man and the image are moving towards each other, we can add their speeds together.

\[ \text{Rate of approach} = \text{Speed of man} + \text{Speed of image} \]

Substituting the values:

\[ \text{Rate of approach} = 2 \, \text{m/s} + 2 \, \text{m/s} = 4 \, \text{m/s} \]

### Conclusion
The man approaches his image at a rate of 4 m/s.

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