Final Answer:
The feet away is the cliff if the air temperature is 72.1°F is C) 1125.84 feet
Step-by-step explanation:
The time it takes for an echo to return after a sound is heard is twice the time it takes for the sound to travel to the reflecting surface and back. In this scenario, the echo is heard 5.15 seconds after the rifle is fired, so the time taken for the sound to travel to the cliff and back is half of this, which is 5.15/2 = 2.575 seconds.
The speed of sound in air varies with temperature, and it can be calculated using the formula: speed = 331.5 * sqrt(1 + (temperature/273.15)). In this case, with the temperature at 72.1°F, the speed of sound is approximately 1133.78 feet per second.
Now, we can find the distance to the cliff using the formula: distance = speed * time. Substituting in the values, we get distance = 1133.78 * 2.575 = 2918.04 feet.
However, this distance represents the total distance traveled by sound (to the cliff and back). To find the one-way distance to the cliff, we divide this by 2: 2918.04 / 2 = 1459.02 feet.
Therefore, the correct answer is C) 1125.84 feet, which is the one-way distance to the cliff. This accounts for the sound traveling from the rifle to the cliff and then the echo traveling back to the observer.