A flag is mounted on a car moving due North with velocity of `20 km//hr`. Strong winds are blowing due East with velocity of `20km//hr`. The flag will point in direction

Options

A. East
B. North-East
C. South-East
D. South-West

Answer

To solve the problem of determining the direction in which the flag will point, we can break it down step by step:

### Step 1: Understand the velocities involved
- The car is moving due North with a velocity of \(20 \, \text{km/hr}\).
- The wind is blowing due East with a velocity of \(20 \, \text{km/hr}\).

### Step 2: Represent the velocities as vectors
- The velocity of the car can be represented as a vector:
\[ \vec{V}_{\text{car}} = 0 \hat{i} + 20 \hat{j} \, \text{km/hr} \]
(where \(\hat{i}\) represents the East direction and \(\hat{j}\) represents the North direction).

- The velocity of the wind can be represented as:
\[ \vec{V}_{\text{wind}} = 20 \hat{i} + 0 \hat{j} \, \text{km/hr} \]

### Step 3: Determine the effective wind velocity relative to the car
- Since the flag is mounted on the car, we need to consider the wind's effect relative to the car's frame of reference. The car's movement will affect how the wind is perceived.
- The perceived wind velocity in the car's frame can be calculated as:
\[ \vec{V}_{\text{perceived}} = \vec{V}_{\text{wind}} - \vec{V}_{\text{car}} \]
Substituting the vectors:
\[ \vec{V}_{\text{perceived}} = (20 \hat{i} + 0 \hat{j}) - (0 \hat{i} + 20 \hat{j}) = 20 \hat{i} - 20 \hat{j} \]

### Step 4: Analyze the resultant vector
- The resultant vector \( \vec{V}_{\text{perceived}} = 20 \hat{i} - 20 \hat{j} \) indicates that the wind is blowing towards the East (\(20 \hat{i}\)) and also has a component pointing South (\(-20 \hat{j}\)).
- To visualize this, we can plot the vector in a coordinate system where East is positive x-direction and North is positive y-direction.

### Step 5: Determine the direction of the resultant vector
- The vector \(20 \hat{i} - 20 \hat{j}\) can be represented in terms of its magnitude and direction. The components are equal in magnitude (20 km/hr), which means the resultant vector points diagonally.
- The angle of this vector can be calculated using the tangent function:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{-20}{20} = -1 \]
This implies that \(\theta = 45^\circ\) below the positive x-axis (East direction).

### Step 6: Conclusion
- Therefore, the flag will point in the direction of the resultant vector, which is \(45^\circ\) below the East direction, indicating that it points towards the Southeast.

### Final Answer
The flag will point in the Southeast direction.

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