To find the distance between the first and second cliff based on the echoes heard by the soldier, we can use the information about the time it takes for the sound to travel to the cliffs and back.
Step 1: Understand the Echo Times
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Time for the first echo: 2 seconds
- This is the time it takes for the sound to travel to the first cliff and back to the soldier.
Hence, the time for sound to reach the first cliff is: \[ t_1 = \frac{2 \text{ seconds}}{2} = 1 \text{ second} \]
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Time for the second echo: 3 seconds after the first echo, totaling 5 seconds since the gun was fired.
- This is the time for the sound to go to the second cliff and back to the soldier.
Therefore, the time for sound to reach the second cliff is: \[ t_2 = \frac{5 \text{ seconds}}{2} = 2.5 \text{ seconds} \]
Step 2: Calculate Distances
Assuming the speed of sound in air is approximately 343 meters per second, we can calculate the distances to the cliffs.
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Distance to the first cliff (D1): \[ D_1 = \text{speed of sound} \times \text{time to first cliff} = 343 \text{ m/s} \times 1 \text{ s} = 343 \text{ meters} \]
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Distance to the second cliff (D2): \[ D_2 = \text{speed of sound} \times \text{time to second cliff} = 343 \text{ m/s} \times 2.5 \text{ s} = 857.5 \text{ meters} \]
Step 3: Find the Distance Between the Cliffs
To find the distance between the two cliffs, we can subtract the distance to the first cliff from the distance to the second cliff:
\[ \text{Distance between cliffs} = D_2 - D_1 = 857.5 \text{ m} - 343 \text{ m} = 514.5 \text{ meters} \]
Conclusion
The distance between the first cliff and the second cliff is approximately 514.5 meters.