A ship searching for a sunken ship sent a sonar signal and detected an echo after 5 s. If ultrasonic wave travels at 1525 m s⁻¹ in seawater, approximately how far down in the ocean is the wreckage of the sunken ship located?
3812.5 m
Explanation
The textbook context provides Example 10.6, which demonstrates that the time taken to reach an underwater object is half the total time of the returning echo. Applying this principle and the formula Distance = Speed × Time, we divide the 5 s echo time by 2 to get 2.5 s, and multiply by the given speed of 1525 m s⁻¹ to find the depth.
Solution Steps
Step 1: Identify Total time for echo = 5 s and Speed of ultrasonic wave = 1525 m s⁻¹
Step 2: Calculate Time taken to reach the wreckage = Total time / 2 = 5 s / 2 = 2.5 s
Step 3: Calculate Distance = Speed × Time = 1525 m s⁻¹ × 2.5 s = 3812.5 m