Two parallel pillars are `11 km` away from an observer. The minimum distance between the pillars so that they can be seen separately will be

Options

A. `3.2m`
B. `20.8 m`
C. `91.5 m`
D. `183m`

Explanation

To solve the problem of determining the minimum distance between two parallel pillars so that they can be seen separately by an observer 11 km away, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have two pillars that are 11 km away from an observer. We need to find the minimum distance \( d \) between these two pillars such that the observer can see them as separate entities.

2. **Concept of Angular Resolution**:
The human eye has a resolution limit, which is approximately \( 1/60 \) degrees. This means that if the angle subtended by the two pillars at the observer is less than this value, they will appear as one.

3. **Setting up the Angle**:
The angle \( \theta \) subtended by the two pillars at the observer can be expressed as:
\[ \theta = \frac{d}{D} \]
where \( d \) is the distance between the two pillars and \( D \) is the distance from the observer to the pillars (11 km or 11000 meters).

4. **Condition for Separation**:
For the observer to see the pillars separately, the angle \( \theta \) must be greater than \( \frac{1}{60} \) degrees. Therefore, we set up the inequality:
\[ \frac{d}{11000} > \frac{1}{60} \]

5. **Solving for \( d \)**:
Rearranging the inequality gives:
\[ d > 11000 \times \frac{1}{60} \]
Now, calculate \( d \):
\[ d > \frac{11000}{60} \]
\[ d > 183.33 \text{ meters} \]

6. **Converting to Meters**:
Since we want the minimum distance in meters, we find:
\[ d > 183.33 \text{ meters} \]

7. **Final Result**:
The minimum distance between the two pillars so that they can be seen separately is approximately \( 183.33 \) meters.

### Summary:
The minimum distance between the two pillars should be greater than \( 183.33 \) meters for them to be seen separately by an observer located 11 km away.