Question

he earliest radio broadcasts on Earth were emitted about 100 years ago. Approximately where are these initial radio waves now? (Radio waves are a type of radiation, so they travel at the speed of light)

Answer 1

`9.45\cdot 10^(17)m`

Step-by-step explanation:

Radio waves are electromagnetic waves.

Electromagnetic waves travel in a vacuum at the speed of light, which is:

`c=3.0\cdot 10^8 m/s`

Therefore, the distance they cover in a time t is

`d=ct`

where d is the distance covered.

In this problem, the time elapsed is

t = 100 y

Keeping in mind that

`1y=365 d\cdot 24 h \cdot 60 m \cdot 60 s =3.15\cdot 10^7 s`

So the time elapsed in seconds is

`t=(100)(3.15\cdot 10^7)=3.15\cdot 10^9 s`

And therefore, the distance covered by the radio waves in this time is

`d=(3\cdot 10^8)(3.15\cdot 10^9)=9.45\cdot 10^(17)m`