Final answer:
To determine the depth of the ocean below a ship using the time for a sound signal to return and the speed of sound, multiply the sound speed by half the total travel time. Given a speed of 1.5 km/s and a two-way travel time of 10 seconds, the calculation shows the ocean's depth is 7500 meters.
Step-by-step explanation:
To calculate the depth of the ocean below the ship, we will use the two-way travel time of the sound and the known speed of sound in the ocean. Since the speed of sound in the ocean is given as 1.5 km/s, and the two-way travel time is 10 seconds, we can apply the formula: Depth = Speed × (Travel Time / 2). Calculations should be done in compatible units, so we use 1.5 km/s, which is equivalent to 1500 m/s.
First, we find the total distance traveled by the sound wave by multiplying the speed of sound by the travel time:
- Total distance = Speed of sound × Travel time
- Total distance = 1500 m/s × 10 s
- Total distance = 15000 meters
Since this distance is the total distance which includes the travel time to and from the ocean floor, we must divide it by 2 to find the one-way travel distance, which is the depth of the ocean:
- Depth of the ocean = Total distance / 2
- Depth of the ocean = 15000 m / 2
- Depth of the ocean = 7500 meters
Therefore, the depth of the ocean at that point is 7500 meters.