An attack submarine is at a depth of 560 feet below the surface and detects a ship on the surface with its sonar that is at a 1.5 degree angle of elevation. What is the actual distance from the submarine to the ship in yards. Additionally is the sonar travels through sea water at an average velocity of 1500 meters/second, how long will it take in seconds for the sonar signal to get back to the sub after it is releases?

Question

An attack submarine is at a depth of 560 feet below the surface and detects a ship on the surface with its sonar that is at a 1.5 degree angle of elevation. What is the actual distance from the submarine to the ship in yards. Additionally is the sonar travels through sea water at an average velocity of 1500 meters/second, how long will it take in seconds for the sonar signal to get back to the sub after it is releases?

Answer 1

sin1.5deg=560/distance solve for distance....where distance is the actual distance, not horizontal distance. If a torpedo went the horizontal distance, it would be short.

time=2*distanceabove/velocitysound

Answer 2

To find the actual distance from the submarine to the ship in yards, we can use trigonometry and the angle of elevation.

First, let's convert the depth of the submarine from feet to yards. Since 1 yard is equal to 3 feet, the submarine is at a depth of 560/3 = 186.67 yards below the surface.

Now, we can set up a right triangle to represent the situation. The submarine's depth is the opposite side, and the distance from the submarine to the ship is the adjacent side. The angle of elevation, 1.5 degrees, is the angle between these two sides.

The formula to find the adjacent side of a right triangle is:
Adjacent side = Opposite side / tan(angle)

Using this formula, we can calculate the adjacent side:
Adjacent side = 186.67 / tan(1.5 degrees)
Adjacent side ≈ 6670.35 yards

Therefore, the actual distance from the submarine to the ship is approximately 6670.35 yards.

Now, let's calculate the time it will take for the sonar signal to get back to the submarine.

Since the sonar travels through seawater at an average velocity of 1500 meters/second, we need to convert the distance from yards to meters.

1 yard ≈ 0.9144 meters

So, the distance from the submarine to the ship in meters is:
6670.35 yards * 0.9144 meters/yard ≈ 6109.31 meters

To find the time it takes for the sonar signal to travel this distance, we can use the formula:
Time = Distance / Velocity

Time = 6109.31 meters / 1500 meters/second
Time ≈ 4.07 seconds

Therefore, it will take approximately 4.07 seconds for the sonar signal to get back to the submarine after it is released.