Question

Consider the speed of light in another universe to be only 100 m/s. Two cars are traveling along a highway in opposite directions. Person 1 is travelling with speed of 39 m/s, and person 2 is travelling in opposite direction with speed of 31 m/s. How fast does person 1 measure person 2 to be traveling? How fast does person 2 measure person 1 to be traveling?

Answer 1

-62.45m/s and +62.45m/s

Step-by-step explanation:

The formula for relativistic speed

This is the speed of A with respect to B

`V_(AB)=(V_(A)-V_(B))/(1-(V_(A)V_(B))/(C^2) )`

where

`V_(A)` will be the velocity of person 1: 39m/s

`V_(B)` will be the velocity of person 2: -31m/s (negative because is travelling in opposite direction)

and
`C` the velocity of light: 100m/s

The velocity of person 1 measured by person 2 is:

`V_(AB)=(39m/s-(-31m/s))/(1-((39m/s)(-31m/s))/((100m/s)^2))=62.45m/s`

The velocity of person 2 measured by person 1 is:

`V_(BA)=(V_(B)-V_(A))/(1-(V_(B)V_(A))/(C^2) )`

`V_(BA)=(-31m/s-39m/s)/(1-((-31m/s)(39m/s))/((100)^2) )=-62.45m/s`