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## A circular radar antenna on a Coast Guard ship has a diameter of 2.10 m and radiates at a frequency of 16.0 GHz. Two small boats are located

Question

A circular radar antenna on a Coast Guard ship has a diameter of 2.10 m and radiates at a frequency of 16.0 GHz. Two small boats are located 7.00 km away from the ship. How close together could the boats be and still be detected as two objects

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Physics
3 years
2021-08-30T23:13:28+00:00
2021-08-30T23:13:28+00:00 1 Answers
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## Answers ( )

Answer:d = 76.5 mExplanation:To find the distance at which the boats will be detected as two objects, we need to use the following equation:Where:θ: is the angle of resolution of a circular aperture

λ: is the wavelength

D: is the diameter of the antenna = 2.10 m

d: is the separation of the two boats = ?

L: is the distance of the two boats from the ship = 7.00 km = 7000 m

To find λ we can use the following equation:

Where:c: is the speed of light = 3.00×10⁸ m/s

f: is the frequency = 16.0 GHz = 16.0×10⁹ Hz

Hence, the distance is:Therefore, the boats could be at 76.5 m close together to be detected as two objects.I hope it helps you!