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

Answer:

-62.45m/s and +62.45m/s

Explanation:

The formula for relativistic speed

This is the speed of A with respect to B

$V_{AB}=\frac{V_{A}-V_{B}}{1-\frac{V_{A}V_{B}}{C^2} }$

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:

$V_{AB}=\frac{39m/s-(-31m/s)}{1-\frac{(39m/s)(-31m/s)}{(100m/s)^2}}=62.45m/s$

The velocity of person 2 measured by person 1 is:

$V_{BA}=\frac{V_{B}-V_{A}}{1-\frac{V_{B}V_{A}}{C^2} }$

$V_{BA}=\frac{-31m/s-39m/s}{1-\frac{(-31m/s)(39m/s)}{(100)^2} }=-62.45m/s$