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# Lightning-fast Measurement: Exploring the Ratio Between Galileo's Time and Human Reaction Time

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Question: Given that the speed of light is 3 x 10^8 m/s and the total distance covered by the light is the round trip between the two hilltops, i.e., 2.9 km x 2 = 5.8 km = 5800 m, The time for light to travel this distance can be calculated by the formula: Time = Distance / Speed Substituting the given values: Time = 5800 m / (3 x 10^8 m/s) = 0.00001933333 seconds Convert seconds to microseconds (µs) by multiplying by 1000000 (since there are 1,000,000 microseconds in one second): Time = 0.00001933333 sec x 1 000 000 µs/sec = 19.33 µs Therefore, Galileo would need to measure a time difference of approximately 19.33 µs for his method to be successful. Now what is the ratio of this time to humsn reaction, which is about 0.2 s.

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The ratio of the time for light to travel the total distance to the average human reaction time can be calculated using the formula: Ratio = Time_Light / Time_Human Substituting the given values: Ratio = 19.33 µs / 0.2 s First, convert the human reaction time to microseconds for the units to match: 0.2 s × 1,000,000 µs/s = 200,000 µs Ratio = 19.33 µs / 200,000 µs = 0.00009665 Therefore, the ratio of the time it takes for light to travel the round trip between the two hilltops to the average human reaction time is approximately 0.00009665 - a dramatically small ratio, indicating the method's impracticability for humans due to our slow reaction times in comparison to the speed of light.

Feb. 8, 2024, 8:10 a.m.

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