In a submarine fitted with a SONAR, the time interval between the generation of an ultrasonic wave and the receipt of its echo is 200 s. What is the distance of the enemy submarine ? The speed of sound in water is 1.450km s⁻¹.

The correct option is 145 km.

Let us understand why this is the correct answer step-by-step.

Step 1: Understand the Physics of SONAR Echoes
A SONAR system works by transmitting an ultrasonic wave from the transmitter on the submarine, which travels through the water, hits the target (the enemy submarine), and reflects back to the receiver of the submarine. This process is called echoing.
Since the sound wave travels to the enemy submarine and back, the total distance covered by the wave is twice the actual distance ($d$) between the two submarines. Therefore, the total distance travelled by the sound wave is $2d$.

Step 2: Identify the Given Values
From the question, we are given:
• Total time interval for the round trip of the wave, $t=200\text{s}$
• Speed of sound in water, $v=1.450{\text{km s}}^{-1}$ (or $1.45\text{km/s}$)

Step 3: Relate Speed, Distance, and Time
We know the basic relationship between speed, distance, and time:
$\text{Speed}=\frac{\text{Total Distance Travelled}}{\text{Time Taken}}$
Substituting our terms into the equation:
$v=\frac{2d}{t}$

Step 4: Solve for Distance ($d$)
Rearranging the formula to find the distance $d$:
$d=\frac{v\times t}{2}$

Now, substitute the given values:
$d=\frac{1.450\text{km/s}\times 200\text{s}}{2}$

Simplify the expression:
$d=1.450\times 100\text{km}$
$d=145\text{km}$

Thus, the distance of the enemy submarine is 145 km.