Question

An observer in frame S′ is moving to the right (+x-direction) at speed u = 0.600c away from a stationary observer in frame S. The observer in S′ measures the speed v′ of a particle moving to the right away from her. What speed v does the observer in S measure for the particle if (a) v′=0.400c; (b) v′=0.900c; (c) v′=0.990c?

Answer 1

a) 0.806c

b) 0.97c

c) 0.997c

Step-by-step explanation:

given:

`v_(x)'=v'\\ v_(x) =v`

solution:

a)
`v=(v'+u)/(1+(uv')/(c^2) )= (0.400+0.600)/(1+(0.400)(0.600) )=0.806c`

b)
`v=(v'+u)/(1+(uv')/(c^2) )= (0.900+0.600)/(1+(0.900)(0.600) )=0.97c`

c)
`v=(v'+u)/(1+(uv')/(c^2) )= (0.99+0.600)/(1+(0.99)(0.600) )=0.997c`