Question

solve all the exercises please

Relativistic Velocity Transformations 7.12. An observer in rocket A finds that rockets C and B are moving away from him in opposite directions at speeds of 0.6c and 0.8c, respectively. What is the speed of C as measured by B? Ans. 0.946c (classically, 1.4c) 7.14. A man standing on the platform of a space station observes two rocket ships approaching him from opposite directions at speeds of 0.9c and 0.8c. At what speed does one rocket ship move with respect to the other? Ans. 0.988C 7.15. Derive the Lorentz velocity transformations for the y- and z-directions.

Answer 1

Problem 7.12

Speed of C with respect to A = V_CA = 0.6c

Speed of B with respect to A = V_BA = 0.8c

Therefore Speed C with respect to B = V_CB

$= \frac{v_{CA} + v_{BA}}{1+\frac{v_{CA}\times v_{BA}}{c^{2}}}$

$= \frac{0.6c + 0.8c}{1+\frac{0.6c\times 0.8c}{c^{2}}} = 0.946c$

Problem 7.14

Speed of Rocket 1 with respect to man = V_RM = 0.9c

Speed of Rocket 2 with respect to man = V_rM = 0.8c

Therefore Rocket 1 with respect to Rocket 2 = V_Rr

$= \frac{v_{RM} + v_{rM}}{1+\frac{v_{RM}\times v_{rM}}{c^{2}}}$

$= \frac{0.9c + 0.8c}{1+\frac{0.9c\times 0.8c}{c^{2}}} = 0.988c$

Problem 7.15

from Lorenta transformation of space ļ time co-ordinates: dy = dy' :. ly dy dt ; dz = dz' & dt w (at' + m dx') dy' dy'ldt' M(dt' tu ndx') ^ (1+ en uý ^1 + ) dx' ly Similarly dz. Uz C dt dz ridt 't _dx') dz'/dt' 7(14 11 v da' C² dt dz Uz r11+ uy