A car driving at a constant speed of `25" m s"^(-1)` heads straight to a mountain. The driver presses the car horn and receives. an echo 3.6 seconds later. Calculate the distance between the car and the mountain when the driver pressed the horn. (Take the speed of sound in air to be `300" m s"^(-1)` )

Options

A. 1080 m
B. 585 m
C. 495 m
D. 90 m

Explanation

To solve the problem, we need to determine the distance between the car and the mountain when the driver pressed the horn. The echo received 3.6 seconds later gives us the necessary information to calculate this distance.

### Step-by-Step Solution:

1. **Understanding the Echo**:
When the driver presses the horn, the sound travels to the mountain and then reflects back to the car. The total time for this round trip is given as 3.6 seconds.

2. **Calculating the Distance Traveled by Sound**:
The speed of sound in air is given as 300 m/s. To find the total distance traveled by the sound in 3.6 seconds, we use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ \text{Distance} = 300 \, \text{m/s} \times 3.6 \, \text{s} = 1080 \, \text{meters} \]
This distance is the total distance for the sound to travel to the mountain and back.

3. **Calculating the Distance to the Mountain**:
Since the distance calculated is for the round trip (to the mountain and back), we need to divide this distance by 2 to find the one-way distance to the mountain:
\[ \text{Distance to the mountain} = \frac{1080 \, \text{meters}}{2} = 540 \, \text{meters} \]

4. **Calculating the Distance the Car Traveled**:
While the sound is traveling, the car is also moving towards the mountain. The speed of the car is given as 25 m/s. We need to calculate how far the car has traveled in the 3.6 seconds:
\[ \text{Distance traveled by car} = \text{Speed} \times \text{Time} \]
\[ \text{Distance traveled by car} = 25 \, \text{m/s} \times 3.6 \, \text{s} = 90 \, \text{meters} \]

5. **Calculating the Initial Distance Between the Car and the Mountain**:
The initial distance between the car and the mountain when the horn was pressed can be calculated by adding the distance to the mountain after the car has moved:
\[ \text{Initial distance} = \text{Distance to the mountain} + \text{Distance traveled by car} \]
\[ \text{Initial distance} = 540 \, \text{meters} + 90 \, \text{meters} = 630 \, \text{meters} \]

### Final Answer:
The distance between the car and the mountain when the driver pressed the horn is **630 meters**.