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Answer :
Final answer:
To find the time elapsed between seeing and hearing an event 521 meters away at 27.6°C, calculate the speed of sound for that temperature and divide the distance by that speed. The calculated time is approximately 1.50 seconds, which does not match any of the available options provided. None of the provided options is correct. The correct answer is 1.4988 s.
Explanation:
To calculate the time elapsed between seeing and hearing an event that is 521 meters away in air at 27.6°C, first we need to determine the speed of sound at that temperature using the provided formula:
v = 331 m/s + (0.6 m/s/°C) * T
v = 331 m/s + (0.6 m/s/°C) * 27.6°C
v = 331 m/s + 16.56 m/s
v = 347.56 m/s
Since the speed of light is much faster than the speed of sound (300,000 km/s), the time taken for light to reach us can be considered instantaneous for this distance. Therefore, the time delay we are calculating is solely due to the speed of sound. To calculate this time delay, we divide the distance by the speed of sound in air at the given temperature:
Time = Distance / Speed of Sound = 521 m / 347.56 m/s
Time ≈ 1.4988 s
The closest answer to our calculation is 1.81 s considering the choices given. However, the correct calculation is ≈1.50 s, which is not an available option. It seems there might be a typo or error in the provided choices.
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