Question

Two astronauts are 1.40 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 328 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

The spaceship is placed at a distance of
`1.28* 10^6\` meters from the Earth.

Step-by-step explanation:

Distance between two astronauts, d = 1.4 m

The time it takes for sound waves to travel at 328 m/s through the air between the astronauts equals the time it takes for the electromagnetic waves to travel to the earth.

For sound, time taken is given by :

`t=(1.4)/(328)\ ........(1)`

For electromagnetic wave, time taken to travel the Earth is :

`t=(d)/(3* 10^8)\ ........(2)`

d is the distance from the Earth to the spaceship.

As time are same :

`(d)/(3* 10^8)=(1.4)/(328)`

`d=(1.4)/(328)* 3* 10^8\\\\d=1.28* 10^6\ m`

So, the spaceship is placed at a distance of
`1.28* 10^6` meters from the Earth.