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A ship emits a sonar signal and blows its foghorn simultaneously. A passing ship picks up the sonar signal and hears the foghorn 12 s later. How far away are the ships if it is 22°C, and the speed of the sonar signal in water is 1450m/s?

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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.

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