The velocity of image object and mirror both are moving towards each other with velocities `4ms^(-1) and 5ms^(-1)` respectively, is

Options

A. `-14ms^(-1)`
B. `15ms^(-1)`
C. `-9ms^(-1)`
D. `14ms^(-1)`

Explanation

To solve the problem of finding the velocity of the image when both the object and the mirror are moving towards each other, we can follow these steps:

### Step 1: Understand the velocities
- The object is moving towards the mirror with a velocity of \( v_o = 4 \, \text{m/s} \).
- The mirror is moving towards the object with a velocity of \( v_m = 5 \, \text{m/s} \).

### Step 2: Set up the relationship
When both the object and the mirror are moving towards each other, the velocity of the object with respect to the mirror can be expressed as:
\[ v_{om} = v_o + v_m \]
where \( v_{om} \) is the velocity of the object with respect to the mirror.

### Step 3: Calculate the velocity of the object with respect to the mirror
Substituting the values:
\[ v_{om} = 4 \, \text{m/s} + 5 \, \text{m/s} = 9 \, \text{m/s} \]

### Step 4: Relate the velocities of the object and the image
According to the mirror formula, the velocity of the object with respect to the mirror is equal and opposite to the velocity of the image with respect to the mirror:
\[ v_{om} = -v_{im} \]
where \( v_{im} \) is the velocity of the image with respect to the mirror.

### Step 5: Solve for the velocity of the image
From the previous relationship:
\[ 9 \, \text{m/s} = -v_{im} \]
Thus,
\[ v_{im} = -9 \, \text{m/s} \]

### Conclusion
The velocity of the image is \( -9 \, \text{m/s} \). The negative sign indicates that the image is moving in the opposite direction to the defined positive direction (which is towards the mirror).

### Final Answer
The velocity of the image is \( -9 \, \text{m/s} \).

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