A horizontal wid is blowing with a velocity `v` towards north-east. A man starts running towards north with acceleration `a`. The after which man will feel the wind blowing towards east is

Options

A. `v/a`
B. `(sqrt(2)V)/a`
C. `v/(sqrt(2)a)`
D. `(2v)/a`

Answer

To solve the problem, we need to determine the time after which the man running towards the north will feel the wind blowing only towards the east. This occurs when the northward component of the wind's velocity equals the man's velocity in the northward direction.

### Step-by-Step Solution:

1. **Understand the Wind's Velocity**:
The wind is blowing towards the north-east with a velocity `v`. We can break this velocity into its components:
- The northward component (y-direction) of the wind's velocity is:
\[ v_y = \frac{v}{\sqrt{2}} \]
- The eastward component (x-direction) of the wind's velocity is:
\[ v_x = \frac{v}{\sqrt{2}} \]

2. **Man's Motion**:
The man starts running towards the north with an acceleration `a`. Since he starts from rest, his velocity at time `t` can be expressed using the equation of motion:
\[ v_m = a t \]

3. **Condition for Feeling Wind Only Towards East**:
The man will feel the wind blowing only towards the east when the northward component of the wind's velocity equals the man's velocity. Therefore, we set the northward component of the wind's velocity equal to the man's velocity:
\[ v_y = v_m \]
Substituting the expressions we have:
\[ \frac{v}{\sqrt{2}} = a t \]

4. **Solve for Time `t`**:
Rearranging the equation to solve for `t` gives:
\[ t = \frac{v}{\sqrt{2} a} \]

### Final Answer:
The time after which the man will feel the wind blowing only towards the east is:
\[ t = \frac{v}{\sqrt{2} a} \]