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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Thu Nguyệt 3 years 2021-08-30T23:13:28+00:00 1 Answers 16 views 0

Answers ( )

  1. Xavia
    0
    2021-08-30T23:14:38+00:00
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    Answer:

    d = 76.5 m

    Explanation:

    To find the distance at which the boats will be detected as two objects, we need to use the following equation:

    \theta = \frac{1.22 \lambda}{D} = \frac{d}{L}

    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:

    \lambda = \frac{c}{f}

    Where:

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

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

    \lambda = \frac{c}{f} = \frac{3.00 \cdot 10^{8} m/s}{16.0 \cdot 10^{9} s^{-1}} = 0.0188 m            

    Hence, the distance is:

    d = \frac{1.22 \lambda L}{D} = \frac{1.22*0.0188 m*7000 m}{2.10 m} = 76.5 m

    Therefore, the boats could be at 76.5 m close together to be detected as two objects.

     

    I hope it helps you!

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