Question

Radio waves of speed $3 \times {10^8} $m/s are reflected off the moon and received back on earth. The time elapsed between the sending of the signal and receiving it back at the earth station is 2.5s. What is the distance of the moon from the earth (in km)?
$A) 8.75 \times {10^5}$km
$B) 3.75 \times {10^4}$km
$C) 3.75 \times {10^5}$km
$D) 8.75 \times {10^4}$km

Answer 1

Hint: According to the question the signal sending to the moon and received back on earth. In the question speed and time values are given so, apply the speed formula to find a total distance. As the question says, the distance of the moon will be half of the total distance.

Formula used:
$d = V \times t$

Complete answer:
$d = V \times t$
Where d is the distance, V is the speed, and t is time.
First, we have to write the given values.
V = $3 \times {10^8}m/\sec $
t = 2.5 sec
Total distance = Speed × Time
substituting given values we get.
$ \Rightarrow d = 3 \times {10^8} \times 2.5s$
$\therefore d = 7.5 \times {10^8}m$
as the question says the distance of the moon will be half of the total distance.
Distance of the moon $ = \dfrac{{7.5 \times {{10}^8}}}{2}$
$\therefore $Distance of the moon from the earth = $3.75 \times {10^8}$ m
Hence the distance between moon and earth will be $3.75 \times {10^8}$m.
We can write it in km as asked in the question.
$\therefore $$3.75 \times {10^5}$km

Hence, the correct answer is given in option C.

Additional information:
Radio waves have various types of frequencies that contain different qualities of propagation in the earth’s environment.
How fast radio waves wavelength travel is that it depends on what they are traveling through, in the vacuum or air the speed of radio is quickest as the speed of light.
Radio waves can be measured in the unit of Hertz; we can write it as Hz. Because scientist Heinrich Hertz exhibited the radio waves.
Radio waves are widely used in TV, standard communication radio, cell communication, airport regulation, and even remote control toys.

Note:
Here we have to count radio signals traveled the same distance two times i.e first is sending signals and receiving signals back. So, during the trip the distance traveled by the signal is 2x.