Question

The radar system of a navy cruiser transmits at a wavelength of 2.0 cm, from a circular antenna with a diameter of 2.0 m. At a range of 7.8 km, what is the smallest distance in meters that two speedboats can be from each other and still be resolved as two separate objects by the radar system?

Answer 1

Answer:

95.16 m

Explanation:

L = Range of radar = 7.8 km

$\lambda$ = Wavelength = 2 cm

d = Diameter of antenna = 2 m

D = Distance

We have the relation

$\dfrac{D}{L}=1.22\dfrac{\lambda}{d}\\\Rightarrow D=1.22\dfrac{L\lambda}{d}\\\Rightarrow D=1.22\dfrac{7800\times 0.02}{2}\\\Rightarrow D=95.16\ m$

The smallest distance in meters that two speedboats can be from each other and still be resolved as two separate objects by the radar system is 95.16 m