A radio wave will travel a distance of three nautical miles in approximately 18.51 microseconds.

The speed of light in a vacuum is approximately 299,792 kilometers per second (km/s) or 186,282 miles per second (mi/s). To convert this speed to nautical miles per microsecond, we use the following calculation:

Speed of light in nautical miles per microsecond = (Speed of light in miles per second) / (1.15078 nautical miles per mile) / (1,000,000 microseconds per second)

Speed of light in nautical miles per microsecond ≈ 186,282 mi/s / 1.15078 nm/mi / 1,000,000 µs/s ≈ 162.58 nm/µs

Now, to find the time it takes for a radio wave to travel a distance of three nautical miles, we use the formula:

Time (in microseconds) = Distance (in nautical miles) / Speed (in nautical miles per microsecond) Time (in microseconds) = 3 nm / 162.58 nm/µs ≈ 0.01851 µs ≈ 18.51 microseconds

Mnemonic: "Nautical Time"

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Each nautical mile traveled at the speed of light (161826 miles per second), takes approx 6 microseconds (1/161282). So a round trip takes approximately 12 microseconds to see the returned RADAR response

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The correct answer is the only one with metric units.

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To get the answer we need to use the correct speed of light in a vacuum, which is approximately 299,792,458 meters per second.

Calculate the time it takes for the RADAR echo to be received back at the antenna when the target is 5 nautical miles away.

Step 1: Convert 5 nautical miles to meters: 5 nautical miles ≈ 5 * 1852 meters per nautical mile ≈ 9260 meters

Step 2: Calculate the time: Time = 2 * (Distance / Speed) Time = 2 * (9260 meters / 299,792,458 meters per second)

Time ≈ 2 * 0.000030873 seconds

Converting this time to microseconds (since 1 second = 1,000,000 microseconds):

Time ≈ 2 * 0.000030873 seconds * 1,000,000 microseconds per second Time ≈ 61.746 microseconds

The correct answer is approximately 61.746 microseconds for the RADAR echo to be received back at the antenna when the target is 5 nautical miles away.

Mnemonic: "RoundTripTime"

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To calculate the time it takes for a RADAR pulse to travel to a target 10 nautical miles away and return to the RADAR receiver, we'll use the speed of light in a vacuum, which is approximately 299,792,458 meters per second.

Step 1: Convert 10 nautical miles to meters: 10 nautical miles ≈ 10 * 1852 meters per nautical mile ≈ 18,520 meters

Step 2: Calculate the time: Time = 2 * (Distance / Speed) Time = 2 * (18,520 meters / 299,792,458 meters per second)

Time ≈ 2 * 0.000061760 seconds

Converting this time to microseconds (since 1 second = 1,000,000 microseconds):

Time ≈ 2 * 0.000061760 seconds * 1,000,000 microseconds per second Time ≈ 123.52 microseconds

The correct answer is approximately 123.52 microseconds for the RADAR pulse to travel to a target 10 nautical miles away and return to the RADAR receiver.

One-word mnemonic: "RoundTripTime"

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There are 1852 meters in 1 nautical mile and it takes RADAR travels 150 meters in 1 microsecond. Thus, 150 meters/microsecond divided by 1862 meters/mile = ~0.081 miles/microsecond.

Multiply the 0.081 miles/microsecond by 308.5 microseconds to get ~25 nautical miles.

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