# Why can't this speed be measured?

Superman and Supergirl were playing catch. When Superman is moving with a speed of 0.800c relative to Supergirl, he threw a ball to Supergirl with a speed of 0.600c relative to him.

a. What was the speed of the ball as measured by Supergirl?

I tried to solve number 1. heres my approach. let s be the supergirl frame of reference while s' be the frame of reference by superman, heres my diagram

(<--)superman     (--->)ball     supergirl(stay)


so s' is going to the left, so it has negative velocity (-0.8c). vx' is going to the right (+0.6c) . now (vx) velocity of ball with respect to supergirl is (-.13c)

using lorentz transformation, vx is negative, so it means its going to the left and it will never reach supergirl. so it appears that answer for letter a is, its impossible?

thanks

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Why are you assuming that superman is moving to the left while attempting to throw the ball to his right? – Willie Wong Jun 18 '12 at 14:29
i think im wrong, it should be assumed that superman is moving towards supergirl, by doing that, everything is all right. – WantIt Jun 18 '12 at 15:03

Its a very simple relativistic velocity addition problem which you make messy due to the wrong putting of + and - at some places in the relativistic velocity addition equation.if $V$ is the magnitude of velocity of man with respect to girl and $Vb$ the magnitude of velocity of ball with respect to man then you have to put $-Vb$ in the relativistic velocity addition equation to find the velocity of ball with respect to girl and reason behind this is relativistic vector transformation of the co-ordinate Axis. Hope it will not bother you again.
Dear Abhinav, welcome to Physics.StackExchange. It is usually helpful to use TeX-like commands to typeset mathematical formulae (and especially symbols such as $V$), this also provides some further structure which is often necessary to understand a particular point made. Standard spelling, punctuation and grammar are also quite useful things as they further facilitate understanding, especially for non-native readers. – Claudius Nov 24 '12 at 21:24