A person moves due east at speed 10 m/s and feels the wind is blowing towards south at speed 10 m/s. Find actual velocity of wind flow -

Options

A. 10 S - E
B. ` 10 sqrt(2) W-S`
C. `10 W -S `
D. `10 sqrt(2) S -E `

Answer

To solve the problem of finding the actual velocity of the wind flow, we can break it down into a few clear steps:

### Step 1: Understand the velocities involved
- The person is moving due east at a speed of 10 m/s.
- The person feels the wind blowing towards the south at a speed of 10 m/s.

### Step 2: Set up a coordinate system
- Let's define east as the positive x-direction and north as the positive y-direction.
- Therefore, the velocity of the person can be represented as:
\[ \vec{V}_{\text{person}} = (10 \, \text{m/s}, 0) \]
- The velocity of the wind as felt by the person (wind velocity with respect to the person) is:
\[ \vec{V}_{\text{wind, person}} = (0, -10 \, \text{m/s}) \]

### Step 3: Use the relative velocity equation
- The actual velocity of the wind can be found using the equation:
\[ \vec{V}_{\text{wind}} = \vec{V}_{\text{wind, person}} + \vec{V}_{\text{person}} \]
- Substituting the values:
\[ \vec{V}_{\text{wind}} = (0, -10) + (10, 0) = (10, -10) \, \text{m/s} \]

### Step 4: Calculate the magnitude of the actual wind velocity
- The magnitude of the actual wind velocity can be calculated using the Pythagorean theorem:
\[ |\vec{V}_{\text{wind}}| = \sqrt{(10)^2 + (-10)^2} = \sqrt{100 + 100} = \sqrt{200} = 10\sqrt{2} \, \text{m/s} \]

### Step 5: Determine the direction of the actual wind velocity
- The direction can be found using the tangent function:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{-10}{10} = -1 \]
- Therefore, \( \theta = 45^\circ \) south of east, which means the wind is blowing towards the southeast.

### Final Result
- The actual velocity of the wind flow is:
\[ 10\sqrt{2} \, \text{m/s} \text{ towards the southeast.} \]

---