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Question: In Galileo’s attempt to determine the speed of light, he and his assistant were located on hilltops about 2.9 km apart. Galileo flashed a light and received a return flash from his assistant. If his assistant had an instant reaction, what time difference would Galileo need to be able to measure for his method to be successful? The speed of light is 3 × 10^8 m/s. Answer in units of µs.

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.

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