A dog barks in a park and hears its echo after 0.5 seconds. The sound of its bark got reflected by a nearby building. The sound of speed in air is 346 m/s. The distance between the dog and the building is

Options

A. `86.5` m
B. `80.6` m
C. 75 m
D. `8.65` m

Answer

To find the distance between the dog and the building, we can follow these steps:

### Step 1: Understand the Problem
The dog barks, and the sound travels to the building and then reflects back to the dog. The total time taken for the sound to travel to the building and back is given as 0.5 seconds.

### Step 2: Use the Speed of Sound
The speed of sound in air is given as 346 m/s.

### Step 3: Calculate the Total Distance
Since the sound travels to the building and back, the total distance traveled by the sound is twice the distance from the dog to the building.

Let the distance from the dog to the building be \( x \). Therefore, the total distance traveled by the sound is \( 2x \).

### Step 4: Relate Distance, Speed, and Time
We can use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Here, the total distance is \( 2x \), the speed is 346 m/s, and the time is 0.5 seconds. So we can write:
\[ 2x = 346 \, \text{m/s} \times 0.5 \, \text{s} \]

### Step 5: Calculate \( 2x \)
Calculating the right side:
\[ 2x = 346 \times 0.5 = 173 \, \text{m} \]

### Step 6: Solve for \( x \)
Now, to find the distance \( x \):
\[ x = \frac{173}{2} = 86.5 \, \text{m} \]

### Conclusion
The distance between the dog and the building is **86.5 meters**.

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