Answer: To calculate the distance between the two ships, we can use the fact that sound travels at a constant speed in water. The time it takes for the sound to travel from the emitting ship to the receiving ship is the sum of the time it takes for the sonar signal and the time it takes for the sound of the foghorn to reach the receiving ship.
Let's assume the distance between the two ships is D (in meters).
Time taken for the sonar signal to travel from emitting ship to receiving ship:
Time_sonar = Distance / Speed_sonar
Time taken for the sound of the foghorn to travel from the emitting ship to the receiving ship:
Time_foghorn = Distance / Speed_sound
The total time for both signals to reach the receiving ship is given as 12 seconds:
Total time = Time_sonar + Time_foghorn
Now, let's plug in the values:
Speed_sonar = 1450 m/s
Speed_sound = Speed of sound in air (approximately 343 m/s at 22°C)
Total time = 12 seconds
We'll calculate the speed of sound in air at 22°C first using the formula:
Speed of sound in air (m/s) = 331.5 m/s + (0.606 m/s/°C) * Temperature in Celsius
Speed of sound in air (m/s) = 331.5 m/s + (0.606 m/s/°C) * 22°C = 331.5 m/s + 13.332 m/s ≈ 344.832 m/s
Now, we can calculate the distance between the two ships:
Total time = Time_sonar + Time_foghorn
12 seconds = Distance / 1450 m/s + Distance / 344.832 m/s
To solve for the distance (D), we'll find the common denominator:
12 seconds = (Distance * 344.832 + Distance * 1450) / (1450 * 344.832)
Now, let's solve for D:
12 seconds = (Distance * (344.832 + 1450)) / (1450 * 344.832)
12 seconds * 1450 * 344.832 = Distance * 1794.832
Distance = (12 seconds * 1450 * 344.832) / 1794.832
Distance ≈ 3545.05 meters
Therefore, the two ships are approximately 3545.05 meters (or 3.545 kilometers) away from each other.