A) 750 m
First of all, let's find the wavelength of the microwave. We have
is the frequency
is the speed of light
So the wavelength of the beam is

Now we can use the formula of the single-slit diffraction to find the radius of aperture of the beam:

where
m = 1 since we are interested only in the central fringe
D = 30 km = 30,000 m
a = 2.0 m is the aperture of the antenna (which corresponds to the width of the slit)
Substituting, we find

and so, the diameter is

B) 0.23 W/m^2
First we calculate the area of the surface of the microwave at a distance of 30 km. Since the diameter of the circle is 750 m, the radius is

So the area is

And since the power is

The average intensity is

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:

<u>Where:</u>
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:
<u>Where:</u>
c: is the speed of light = 3.00x10⁸ m/s
f: is the frequency = 16.0 GHz = 16.0x10⁹ Hz
Hence, the distance is:

Therefore, the boats could be at 76.5 m close together to be detected as two objects.
I hope it helps you!
Answer:
A = 4.6 [m²]
Explanation:
The area of a circle can be calculated by means of the following equation.

where:
A = area [m²]
D = diameter = 2.42 [m]
Now replacing:
![A=\frac{\pi }{4} *(2.42)^{2} \\A = 4.6 [m^{2} ]](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20%2A%282.42%29%5E%7B2%7D%20%5C%5CA%20%3D%204.6%20%5Bm%5E%7B2%7D%20%5D)
<span>It is important to use a fixed common reference point on your work peace or drawing to avoid cumulative error</span>