Conversations with astronauts on the lunar surface were characterized by a kind of echo in which the earthbound person’s voice was so loud in the astronaut’s space helmet that it was picked up by the astronaut’s microphone and transmitted back to Earth. It is reasonable to assume that the echo time equals the time necessary for the radio wave to travel from the Earth to the Moon and back (that is, neglecting any time delays in the electronic equipment). Calculate the distance from Earth to the Moon given that the echo time was 2.56 s and that radio waves travel at the speed of light (3.00×10^{8} 8 m/s) (in km).

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migueletorallam migueletorallam · Answer 1 · 2019-09-06T03:53:22+02:00

Answer:

The distance from Earth to Moon in kilometers is [tex]384*10^{3}km[/tex]

Explanation:

Because the radio wave travels at a constant speed, to compute the distance we can use the equation of uniform rectilinear motion:

[tex]d=v*t[/tex]

where [tex]v[/tex] is the speed of the wave, [tex]d[/tex] is the distance it travels and, [tex]t[/tex] is the time it takes to travel that distance.

The radio wave takes 2.56s to go from Earth to the Moon and return and it travels at speed of light.

[tex]v= 3*10^8 \dfrac{m}{s}[/tex]

If we let the distance from Earth to Moon be [tex]d[/tex] our ecuation of uniform rectilinear motion turns into

[tex]2*d=(3*10^{8})*2.56\\d=\dfrac{(3*10^{8})*2.56}{2}\\d=384*10^{6}m[/tex]

We want distance to be in km thats why we need to do a convertion

[tex]d=384*10^{6}m*\dfrac{1km}{1000m}=384*10^{3}km[/tex]

Thus, the distance from Earth to Moon (in kilometers) is

[tex]d=384*10^{3}km[/tex]