A man stands between two cliffs and fires a gun. He hears two successive echoes after 3 s and 5 s. The distance between two cliffs is

Options

A. 1310 m
B. 1320 m
C. 1315 m
D. 1312 m

Explanation

To solve the problem of finding the distance between two cliffs based on the time taken to hear echoes, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- A man stands between two cliffs and fires a gun.
- He hears the first echo after 3 seconds and the second echo after 5 seconds.

2. **Defining Variables**:
- Let \( d_1 \) be the distance from the man to the first cliff (C1).
- Let \( d_2 \) be the distance from the man to the second cliff (C2).
- The total distance between the cliffs \( D = d_1 + d_2 \).

3. **Using the Speed of Sound**:
- The speed of sound in air is approximately \( v = 330 \, \text{m/s} \).
- The time taken for the sound to travel to the first cliff and back is \( t_1 = 3 \, \text{s} \).
- The time taken for the sound to travel to the second cliff and back is \( t_2 = 5 \, \text{s} \).

4. **Setting Up Equations**:
- For the first echo (to C1 and back):
\[ 2d_1 = v \cdot t_1 \implies d_1 = \frac{v \cdot t_1}{2} \]
- For the second echo (to C2 and back):
\[ 2d_2 = v \cdot t_2 \implies d_2 = \frac{v \cdot t_2}{2} \]

5. **Calculating Distances**:
- Substitute \( v = 330 \, \text{m/s} \):
\[ d_1 = \frac{330 \cdot 3}{2} = \frac{990}{2} = 495 \, \text{m} \]
\[ d_2 = \frac{330 \cdot 5}{2} = \frac{1650}{2} = 825 \, \text{m} \]

6. **Finding Total Distance**:
- Now, add \( d_1 \) and \( d_2 \) to find \( D \):
\[ D = d_1 + d_2 = 495 + 825 = 1320 \, \text{m} \]

7. **Final Answer**:
- The distance between the two cliffs is \( 1320 \, \text{m} \).

### Summary:
The distance between the two cliffs is **1320 meters**.