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 5.00 km away from the ship. how close together could the boats be and still be detected as two objects

Answer 1

By definition,
q = 1.22y/D

Where,
q = min. angle
y = wavelength
D = Aperture diameter = diameter of the antenna

At distance "x" from the antenna,
L =xq = 1.22xy/D
Where, L = Min. distance

But, y =c/f = (3*10^8)/(16*10^9) = 0.01875 m

Substituting;
L = 1.22*5*10^3*0.01875/2.1 = 54.46 m