A circular radar antenna on a Coast Guard ship has a diameter of 2.10 m and radiates at a frequency of 11.0 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 11.0 GHz. Two small boats are located 8.00 km away from the ship. How close together could the boats be and still be detected as two objects

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Khánh Gia 6 months 2021-07-21T20:00:58+00:00 1 Answers 5 views 0

Answers ( )

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    2021-07-21T20:02:02+00:00

    Given Information:  

    Frequency = f = 11 Ghz = 11×10⁹  Hz

    Distance between boats = L = 8 km = 8000 m

    Diameter of radar antenna = D = 2.10 m

    Required Information:  

    Distance between boats = d = ?

    Answer:  

    Distance between boats = d = 126.65 m

    Explanation:  

    The minimum distance between the two boats that will result in the detection by the radar antenna is given by

    d = Ltan(θmin)

    Where θmin is given by

    θmin = sin⁻¹(1.22*λ/D)

    Where D is the diameter of the radar antenna and λ is the wavelength given by

    λ = c/f

    Where c is the speed of light

    λ = 3×10⁸/11×10⁹

    λ = 0.02727 m

    θmin = sin⁻¹(1.22*(0.02727)/2.10)

    θmin = 0.907°

    Therefore, the minimum distance between the two boats so that the radar antenna may detect is

    d = 8000*tan(0.907)

    d = 126.65 m

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