IOllow tnereirom. 7. Show that two successive L.T. corresponding to speeds v, and v, are equivalent...

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IOllow tnereirom. 7. Show that two successive L.T. corresponding to speeds v, and v, are equivalent to a single L.T. Vị +V2 corresponding to a speed of v = Vị V2 1+ c2 Hint: Consider three inertial frames S, S', S". Let S' move with speed v, relative to S and let S" move with speed v, relative to S'. Then x = T, (x – v,t) etc. and x" = T,(x – v,t) etc. - Show that x' = r,r2 1+ c2 - (V + v2)t Vị V2 = r,r, 1+ c2 V + v2 -t V V2 1+ c2 34 A Primer of Special Relativity V +v2 「商““ 1 = T(x – vt) where and v = /2 Vị V2 1+ c2 IOllow tnereirom. 7. Show that two successive L.T. corresponding to speeds v, and v, are equivalent to a single L.T. Vị +V2 corresponding to a speed of v = Vị V2 1+ c2 Hint: Consider three inertial frames S, S', S". Let S' move with speed v, relative to S and let S" move with speed v, relative to S'. Then x = T, (x – v,t) etc. and x" = T,(x – v,t) etc. - Show that x' = r,r2 1+ c2 - (V + v2)t Vị V2 = r,r, 1+ c2 V + v2 -t V V2 1+ c2 34 A Primer of Special Relativity V +v2 「商““ 1 = T(x – vt) where and v = /2 Vị V2 1+ c2

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