A person clapped his hands near a cliff and heard echo after 6 s. The distance of the cliff from the person is :
[take v = 346`ms^(- 1)`]

Options

A. 1038 m
B. 1083 m
C. 2076 m
D. 2706 m

Answer

To find the distance of the cliff from the person based on the echo heard after 6 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
- The person clapped his hands, and the echo was heard after 6 seconds. This means the sound traveled to the cliff and back to the person in this time.

2. **Identify Given Values**:
- Time taken for the echo to return, \( T = 6 \) seconds.
- Speed of sound, \( v = 346 \, \text{m/s} \).

3. **Calculate Total Distance Traveled by Sound**:
- The total distance traveled by the sound is given by the formula:
\[ \text{Total Distance} = \text{Speed} \times \text{Time} \]
- Substituting the values:
\[ \text{Total Distance} = 346 \, \text{m/s} \times 6 \, \text{s} = 2076 \, \text{meters} \]

4. **Determine the One-Way Distance to the Cliff**:
- Since the sound travels to the cliff and then back, the distance to the cliff is half of the total distance:
\[ \text{Distance to Cliff} = \frac{\text{Total Distance}}{2} = \frac{2076 \, \text{meters}}{2} = 1038 \, \text{meters} \]

5. **Final Answer**:
- The distance of the cliff from the person is **1038 meters**.