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A radar used to detect the presence of aircraft receives a pulse that has reflected off an object $6 \times 10^{-5} \textrm{ s}$ after it was transmitted. What is the distance from the radar station to the reflecting object?
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Final Answer

$9 \textrm{ km}$

Solution Video

OpenStax College Physics Solution, Chapter 24, Problem 13 (Problems & Exercises) (1:03)

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Video Transcript

This is College Physics Answers with Shaun Dychko. This radar emits a pulse of light and that's reflected-off this aircraft and returns to the radar sometime later. And so we want to find how far is the aircraft from the radar given a certain amount of time it takes to do this round trip; while doing the round trip means doing the trip twice. So covering this distance <i>d</i> twice and so we have 2 times the distance between the aircraft in the radar equals the speed of this wave, which is the speed of light <i>c</i> multiplied by the total time it takes to do the round trip. And so we'll divide both sides by 2 to solve for <i>d</i>. And we get <i>d</i> then is the speed of light 3 times 10 to the 8 meters per second multiplied by the time between emission and detection of the reflected pulse, which is 6 times 10 to the minus 5 seconds and divide that by 2 to get a distance of 9 kilometers and only one significant figure is appropriate here because our time measurement is one significant figure.