Question

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 (3.00×108 m/s). Give your answer in thousands of km.

Answer 1

Answer: 768000km

Explanation:

Velocity is given by the relation between the distance $d$ and the time it takes to travel that distance $t$:

$V=\frac{d}{t}$   (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":

$t=2.56s$  (2)

In addition, we know radio waves are electromagnetic waves (light), and its velocity is:

$V=3(10)^{8}m/s$   (3)

Substituting (2) and (3) in (1):

$3(10)^{8}m/s=\frac{d}{2.56s}$   (4)

And finding $d$:

$d=(3(10)^{8}m/s)(2.56s)$   (5)

Finally we can obtain the distance:

$d=768000000m=768000km$  

Answer 2

Answer:

384,000 km

Explanation:

Given

Velocity of radio wave $v = 3.00 \times 10^{8}m/s$

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

$t = \frac{T}{2}\\\\t = \frac{2.56}{2} \\\\t = 1.28 s$

$v = \frac{d}{t}\\\\d = vt\\\\d = 3 \times 10^8 \times 1.28\\\\d = 3.84 \times 10^8 m\\\\d = 384,000 km$