1. two astronauts are 2.00 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 354 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?
Our values are
We can find the time through
The expression for the distance between the Earth and the spaceship is as follow:
Where c is Light speed, and t our previous time.
Therefore the distance between the Eath and the Spaceship is m
For sound waves we have v=d/t where v is the speed of sound and d the distance between the astronauts, while for electromagnetic waves we have c=D/t where c is the speed of light and D the distance between the spaceship and Earth. We have written both times as the same because is what is imposed by the problem, so we have t=d/v=D/c, which means:
And for our values: