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Answer :
Final answer:
Laser range finders can determine distances with an accuracy depending on the precision of time measurement. When measuring the distance to the Moon, if the time measurement is accurate to 0.100 ns, the distance can be measured to the nearest 10 meters (option a). This accuracy is sufficient for applications like surveying and military operations.
Explanation:
Determining the Accuracy of a Laser Range Finder
Laser range finders can measure distances with remarkable accuracy due to the speed of light's constancy and the precision of modern time-measuring devices. When a laser range finder is used, the distance to the target is determined by measuring the time it takes for a laser beam to travel to the target and back.
The accuracy to which this distance can be measured depends on the precision of the time measurement. For instance, when determining the distance to the Moon with a laser reflecting off a lunar reflector, if the time can be measured to 0.100 nanoseconds (ns), the accuracy of the distance measurement is high.
If we calculate the accuracy for the Moon scenario:
- Speed of light (c) = 299,792,458 meters per second (m/s)
- Measurement precision (Δt) = 0.100 ns = 0.100 x 10-9 seconds
- Accuracy in meters (Δd) = c * Δt = 299,792,458 m/s * 0.100 x 10-9 s = 30 meters
- The average distance to the Moon (L) = 384,400,000 meters
- Percent accuracy = (Δd / L) * 100% = (30 / 384,400,000) * 100% ≈ 0.0000078%
As seen in this example, the accuracy to which distance can be measured is 30 meters, indicating that the correct answer is to the nearest 10 meters. Hence, in applications such as surveying or military operations, where laser range finders are typically employed, the preferred means of determining the observer-target distance may be determined to the nearest 10 meters. However, this can change depending on the specific technology and application in use.
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