At what speed does the image of the boy will approach him in `(ms^(-1))` if he is runing at a speed of 36 kmph towards the mirror ?

Explanation

To determine the speed at which the image of the boy approaches him while he is running towards a mirror, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The speed of the boy is given as 36 km/h. We need to convert this speed into meters per second (m/s) using the conversion factor:
\[ 1 \text{ km/h} = \frac{1}{3.6} \text{ m/s} \]
So, we calculate:
\[ \text{Speed in m/s} = 36 \text{ km/h} \times \frac{1}{3.6} \text{ m/s per km/h} = 10 \text{ m/s} \]

### Step 2: Understand the concept of image formation in a mirror
When the boy runs towards the mirror, his image also moves towards him. The distance between the boy and his image decreases as he approaches the mirror. The speed of the image approaching the boy is equal to the speed of the boy plus the speed of the image itself.

### Step 3: Calculate the speed of the image
The image of the boy in the mirror will also appear to move towards him at the same speed that he is moving towards the mirror. Therefore, if the boy is running at 10 m/s towards the mirror, the image will also approach him at the same speed of 10 m/s.

### Step 4: Total speed of the image approaching the boy
Since the boy is moving towards the mirror at 10 m/s and the image is also moving towards the boy at 10 m/s, the relative speed at which the image approaches the boy is:
\[ \text{Total speed} = \text{Speed of boy} + \text{Speed of image} = 10 \text{ m/s} + 10 \text{ m/s} = 20 \text{ m/s} \]

### Final Answer
Thus, the speed at which the image of the boy approaches him is:
\[ \boxed{20 \text{ m/s}} \]

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