Answer: 768000km
Explanation:
Velocity is given by the relation between the distance [tex]d[/tex] and the time it takes to travel that distance [tex]t[/tex]:
[tex]V=\frac{d}{t}[/tex] (1)
In this problem we are told the time it takes for radio wave to travel from the Earth to the Moon and back is the "echo":
[tex]t=2.56s[/tex] (2)
In addition, we know radio waves are electromagnetic waves (light), and its velocity is:
[tex]V=3(10)^{8}m/s[/tex] (3)
Substituting (2) and (3) in (1):
[tex]3(10)^{8}m/s=\frac{d}{2.56s}[/tex] (4)
And finding [tex]d[/tex]:
[tex]d=(3(10)^{8}m/s)(2.56s)[/tex] (5)
Finally we can obtain the distance:
[tex]d=768000000m=768000km[/tex]
Answer:
384,000 km
Explanation:
Given
Velocity of radio wave [tex]v = 3.00 \times 10^{8}m/s[/tex]
Duration of echo T = 2.56 s
Solution
Time taken for the radio wave to travel to moon and to travel back to earth as it was picked up by the astronaut's microphone is 2.56 s
Since any time delays in the electronic equipment can be ignored
time taken for the radio wave to reach moon
[tex]t = \frac{T}{2}\\\\t = \frac{2.56}{2} \\\\t = 1.28 s[/tex]
[tex]v = \frac{d}{t}\\\\d = vt\\\\d = 3 \times 10^8 \times 1.28\\\\d = 3.84 \times 10^8 m\\\\d = 384,000 km[/tex]
