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:
[tex] \theta = \frac{1.22 \lambda}{D} = \frac{d}{L} [/tex]
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:
[tex] \lambda = \frac{c}{f} [/tex]
Where:
c: is the speed of light = 3.00x10⁸ m/s
f: is the frequency = 16.0 GHz = 16.0x10⁹ Hz
[tex] \lambda = \frac{c}{f} = \frac{3.00 \cdot 10^{8} m/s}{16.0 \cdot 10^{9} s^{-1}} = 0.0188 m [/tex]
Hence, the distance is:
[tex]d = \frac{1.22 \lambda L}{D} = \frac{1.22*0.0188 m*7000 m}{2.10 m} = 76.5 m[/tex]
Therefore, the boats could be at 76.5 m close together to be detected as two objects.
I hope it helps you!
