Given Information:
Frequency = f = 11 Ghz = 11x10⁹ 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 = 3x10⁸/11x10⁹
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
