Superman and Supergirl were playing catch. When Superman is moving with a speed

Question

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

Explanation / Answer

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.

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