A person clapped his hands near a cliff and heard the echo after `5 s`. What is the distance of the cliff from the person if the speed of the sound, `v` is taken as `346 m//s` ?

Explanation

To find the distance of the cliff from the person who clapped his hands and heard the echo after 5 seconds, we can follow these steps:

### Step 1: Understand the Echo
When the person claps, the sound travels to the cliff and then reflects back to the person. The total time taken for the sound to travel to the cliff and back is given as 5 seconds.

### Step 2: Calculate the Total Distance
The total distance traveled by the sound is twice the distance to the cliff (D), because the sound goes to the cliff and returns. Therefore, we can express this as:
\[ \text{Total Distance} = 2D \]

### Step 3: Use the Speed of Sound
The speed of sound (v) is given as 346 m/s. We can use the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Thus, the total distance traveled by the sound can also be expressed as:
\[ \text{Total Distance} = v \times t \]
Where \( t \) is the total time (5 seconds).

### Step 4: Set Up the Equation
Now we can set up the equation:
\[ 2D = v \times t \]
Substituting the known values:
\[ 2D = 346 \, \text{m/s} \times 5 \, \text{s} \]

### Step 5: Calculate the Total Distance
Calculating the right side:
\[ 2D = 346 \times 5 = 1730 \, \text{m} \]

### Step 6: Solve for D
Now, we can solve for D:
\[ D = \frac{1730}{2} = 865 \, \text{m} \]

### Conclusion
The distance of the cliff from the person is **865 meters**.

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