The echo of a gun shot is heard 8 sec. after the gun is fired. How far from him is the surface that reflects the sound (velocity of sound in air = 350 m/s )

Options

A. 1400 m
B. 2800 m
C. 700 m
D. 350 m

Answer

To solve the problem of finding the distance from the observer to the reflecting surface when the echo of a gunshot is heard 8 seconds after the shot is fired, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- The echo is heard after 8 seconds, which means the sound travels to the reflecting surface and back to the observer in this time.

2. **Define Variables**:
- Let \( D \) be the distance from the observer to the reflecting surface.
- The total distance traveled by the sound is \( 2D \) (to the surface and back).

3. **Use the Speed of Sound**:
- The speed of sound in air is given as \( 350 \, \text{m/s} \).

4. **Use the Time Given**:
- The total time taken for the sound to travel to the surface and back is \( 8 \, \text{s} \).

5. **Set Up the Equation**:
- The relationship between distance, speed, and time is given by the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Therefore, for the total distance traveled by the sound:
\[ 2D = \text{Speed} \times \text{Time} \]
- Substituting the known values:
\[ 2D = 350 \, \text{m/s} \times 8 \, \text{s} \]

6. **Calculate the Total Distance**:
- Calculate \( 350 \times 8 \):
\[ 2D = 2800 \, \text{m} \]

7. **Solve for \( D \)**:
- To find \( D \), divide both sides by 2:
\[ D = \frac{2800}{2} = 1400 \, \text{m} \]

8. **Conclusion**:
- The distance from the observer to the reflecting surface is \( 1400 \, \text{m} \).

### Final Answer:
The surface that reflects the sound is \( 1400 \, \text{m} \) away from the observer.

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