A gun is fired on board a ship at sea and an echo is heard from a cliff after the lapse of 9.6 sec. The velocity of sound is 1100 ft/sec. The distance of the cliff from the ship is

Options

A. 1056 feet
B. 5280 feet
C. 10560 feet
D. 21120 feet

Answer

To find the distance of the cliff from the ship, we can follow these steps:

### Step 1: Understand the scenario
When the gun is fired from the ship, the sound travels to the cliff and then reflects back to the ship. The total time taken for this round trip is given as 9.6 seconds.

### Step 2: Determine the total distance traveled by sound
Since the sound travels to the cliff and back, the total distance traveled by the sound is twice the distance from the ship to the cliff. We can denote the distance from the ship to the cliff as \( x \). Therefore, the total distance traveled by the sound is \( 2x \).

### Step 3: Use the formula for distance
The distance traveled by sound can also be calculated using the formula:
\[ \text{Distance} = \text{Velocity} \times \text{Time} \]
Here, the velocity of sound is given as 1100 feet/second, and the total time taken is 9.6 seconds. Thus, we can write:
\[ 2x = 1100 \, \text{ft/sec} \times 9.6 \, \text{sec} \]

### Step 4: Calculate the total distance
Now, we can calculate the total distance:
\[ 2x = 1100 \times 9.6 = 10560 \, \text{feet} \]

### Step 5: Solve for \( x \)
To find the distance from the ship to the cliff, we divide the total distance by 2:
\[ x = \frac{10560}{2} = 5280 \, \text{feet} \]

### Conclusion
Thus, the distance of the cliff from the ship is **5280 feet**.

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