Final answer:
To determine the distance from the ship to the underwater explosion, we can calculate the time it takes for sound to travel in both water and air and add them together. By solving for x in the equations x/4000 + (x+180,000)/1500 = 45, we find that the distance between the ship and the explosion is 247,500 ft.
Step-by-step explanation:
To determine the distance from the ship to the underwater explosion, we need to consider the time it takes for sound to travel in both water and air.
Given that the sound is detected by sonar 45 seconds before it is heard on the deck, we can calculate the total time it takes for sound to travel by adding the time it takes in water and the time it takes in air.
Let's denote the distance between the ship and the explosion as x.
The time it takes for sound to travel through water can be calculated using the equation: time = distance / speed.
In this case, we have: 45 = x / 4000.
Solving for x, we find that the distance in water is 180,000 ft.
The time it takes for sound to travel through air can be calculated in a similar way.
45 = (x + 180,000) / 1500.
Simplifying this equation, we find that the distance in air is 67,500 ft.
Therefore, the total distance between the ship and the explosion is the sum of the distances in water and air:
180,000 + 67,500 = 247,500 ft.