A sonar signal from a ship is emitted underwater towards the sea bed. It takes 0.7 s for the signal to bounce back from the sea bed. If sound travels at 1500 ` m s ^(-1)` in water, how deep is the sea?

Options

A. 525 m
B. 1050 m
C. 1071m
D. 2143 m

Explanation

To find the depth of the sea using the sonar signal information provided, we can follow these steps:

### Step 1: Understand the problem
A sonar signal is emitted from a ship, travels to the sea bed, and then reflects back to the ship. The total time taken for the signal to travel to the sea bed and back is given as 0.7 seconds.

### Step 2: Identify the known values
- Speed of sound in water (v) = 1500 m/s
- Total time taken for the signal to return (t) = 0.7 s

### Step 3: Calculate the total distance traveled by the sound
The total distance traveled by the sound wave is twice the depth of the sea (h), since it goes down to the sea bed and comes back up:
\[ \text{Total distance} (s) = 2h \]

### Step 4: Use the formula for speed
The formula for speed is given by:
\[ v = \frac{s}{t} \]
Rearranging this formula to find the distance (s):
\[ s = v \cdot t \]

### Step 5: Substitute the known values into the equation
Substituting the values of speed and time into the equation:
\[ s = 1500 \, \text{m/s} \times 0.7 \, \text{s} \]
\[ s = 1050 \, \text{m} \]

### Step 6: Relate the total distance to the depth
Since the total distance \( s \) is equal to \( 2h \):
\[ 2h = 1050 \, \text{m} \]

### Step 7: Solve for the depth (h)
To find the depth \( h \):
\[ h = \frac{1050 \, \text{m}}{2} \]
\[ h = 525 \, \text{m} \]

### Final Answer
The depth of the sea is **525 meters**.

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