Question

Two astronauts are 2.70 m apart in their spaceship. One speaks to the other. The conversation is transmitted to earth via electromagnetic waves. The time it takes for sound waves to travel at 343 m/s through the air between the astronauts equals the time it takes for the electromagnetic waves to travel to the earth. How far away from the earth is the spaceship

Answer 1

To solve this problem it is necessary to apply the concepts related to the kinematic equations of linear motion. For this purpose, we will use the definition of the speed equivalent to the displacement made by a body in a fraction of time. From this definition we will relate the time and distance variables required in the problem

$v = \frac{d}{t} \rightarrow t = \frac{d}{v}$

Here,

v = Velocity

d = Distance

t = Time

With our values we have,

$t = \frac{2.7}{343}$

$t = 0.007871s$

The speed of light is the speed at which waves move, therefore using the same formula above, but to find the distance we would have

$d = ct$

Here,

c = Speed velocity

We have then,

$d = (3*10^8m/s)(0.007871s)$

$d = 2.3613*10^6m$

Therefore the distance between the Earth and the spaceship is $2.3613*10^6m$