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## Homework Statement

Two spaceships pass each other. Spaceship A moves relative to nearby planet at velocity v

_{1}, while spaceship B moves at velocity v

_{2}relative to the planet . How fast does spaceship A moves relative to spaceship B.

## Homework Equations

Velocity Transformation : v

^{*}= (v-u)/(1-(vu/c

^{2}))

Inverse Velocity Transformation : v= (v

^{*}+u)/(1+(v

^{*}u/c

^{2}))

## The Attempt at a Solution

Let planet be the S frame

Let spaceship B be the S

^{*}frame

Let spaceship A be the event

Then,

v= velocity of event according to S frame ( here planet)

v

^{*}= velocity of the event according to S

^{*}frame (Here spaceship B)

u= relative velocity of S

^{*}frame wrt to S frame

event = Spaceship A

Using these :

v= v

_{1}

u=-v

_{2}

v

^{*}= V (which we have to find)

Using the inverse velocity transformation I get the solution :

V= v

_{1}+v

_{2}/(1+(v

_{1}v

_{2}/c

^{2}))

But correct solution given in the text book is

V = |v

_{1}-v

_{2}|/(1-(v

_{1}v

_{2}/c

^{2})

Can some one help me with this ! :)