Assertion: An observer is moving due east and wind appears him to blow from north. Then the actual direction of air blow must be towards south-east
Reason: `vecV_(R)=vecV_(A)-vecV_(M)` where `vecV_(R)` is the relative velocity of wind w.r.t. man. `vecV_(A)=` actual velocity of wind (w.r.t. ground) and `vecV_(M)=` velocity of man w.r.t. ground.

Options

A. If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.
B. If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.
C. If Assertion is Trie but the Reason is False.
D. If both Assertion `&` Reason are false

Answer

To solve the problem, we need to analyze the motion of the observer and the wind using vector addition. Let's break down the steps:

### Step 1: Understand the scenario
The observer is moving due east, which we can represent as the positive x-direction. The wind appears to blow from the north, which means that the observer perceives the wind coming from the negative y-direction.

### Step 2: Define the velocities
- Let the velocity of the observer (man) be represented as \( \vec{V}_M = v_M \hat{i} \), where \( v_M \) is the speed of the observer moving east.
- The wind appears to blow from the north, which we can represent as \( \vec{V}_R = -v_W \hat{j} \), where \( v_W \) is the speed of the wind.

### Step 3: Use the relative velocity equation
According to the problem, the relative velocity of the wind with respect to the observer is given by:
\[ \vec{V}_R = \vec{V}_A - \vec{V}_M \]
Where:
- \( \vec{V}_R \) is the relative velocity of the wind with respect to the observer.
- \( \vec{V}_A \) is the actual velocity of the wind (with respect to the ground).
- \( \vec{V}_M \) is the velocity of the observer.

### Step 4: Set up the equation
From the above definitions, we can rewrite the equation as:
\[ -v_W \hat{j} = \vec{V}_A - v_M \hat{i} \]
Rearranging gives us:
\[ \vec{V}_A = v_M \hat{i} - v_W \hat{j} \]

### Step 5: Determine the actual direction of the wind
The actual velocity of the wind \( \vec{V}_A \) can be represented as:
\[ \vec{V}_A = v_M \hat{i} - v_W \hat{j} \]
This indicates that the wind has both an eastward (positive x) and a southward (negative y) component.

### Step 6: Analyze the direction
To find the actual direction of the wind, we can visualize the vector \( \vec{V}_A \):
- The eastward component is \( v_M \hat{i} \).
- The southward component is \( -v_W \hat{j} \).

The resultant vector will point towards the southeast quadrant because it has a positive x-component and a negative y-component.

### Conclusion
Thus, the actual direction of the wind must indeed be towards the southeast.