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

we know that center of mass is given as
r = (m₁
+ m₂
)/(m₁ + m₂)
taking derivative both side relative to "t"
dr/dt = (m₁ d
/dt + m₂ d
/dt)/(m₁ + m₂)
v = (m₁
+ m₂
)/(m₁ + m₂)
taking derivative again relative to "t" both side
dv/dt = (m₁ d
/dt + m₂ d
/dt)/(m₁ + m₂)
a= (m₁
+ m₂
)/(m₁ + m₂)
During a total lunar eclipse, the Moon located in the umbra.
The answer is letter A. For a total lunar eclipse to occur, the Sun, Earth and
Moon must be aligned in a straight line. The Earth’s umbra complete covers the
Moon. The earth’s umbra is about 870,000 miles wide.