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

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