A pandubbi sends a sonar signal to locate a body and receives the echo after 5 s. If the velocity of sound is 340 m/s. What is the distance of the body?

Options

A. 0.85 km
B. 3.5 km
C. 0.425 km
D. 4.25 km

Explanation

To solve the problem of finding the distance of the body from the Pandubbi using the sonar signal, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
- A sonar signal is sent out by the Pandubbi and the echo is received after 5 seconds.
- The speed of sound in water is given as 340 m/s.

2. **Identify the Total Distance Traveled**:
- When the sonar signal is sent, it travels to the body and then returns back to the Pandubbi.
- Therefore, the total distance traveled by the sound is twice the distance to the body (d).
- This can be expressed as:
\[ D = 2d \]
where \(D\) is the total distance traveled.

3. **Use the Formula for Speed**:
- The speed of sound can be expressed using the formula:
\[ v = \frac{D}{t} \]
where \(v\) is the speed of sound, \(D\) is the total distance, and \(t\) is the time taken.

4. **Rearranging the Formula**:
- We can rearrange the formula to find the distance to the body:
\[ D = v \times t \]
- Since \(D = 2d\), we can substitute to find:
\[ 2d = v \times t \]
- Therefore, the distance to the body (d) can be expressed as:
\[ d = \frac{v \times t}{2} \]

5. **Substituting the Values**:
- Now we can substitute the known values into the equation:
- \(v = 340 \, \text{m/s}\)
- \(t = 5 \, \text{s}\)
- Thus:
\[ d = \frac{340 \, \text{m/s} \times 5 \, \text{s}}{2} \]

6. **Calculating the Distance**:
- Calculate the numerator:
\[ 340 \times 5 = 1700 \, \text{m} \]
- Now divide by 2:
\[ d = \frac{1700}{2} = 850 \, \text{m} \]

7. **Convert to Kilometers**:
- To convert meters to kilometers, divide by 1000:
\[ d = \frac{850}{1000} = 0.85 \, \text{km} \]

8. **Final Answer**:
- The distance of the body from the Pandubbi is **0.85 km**.