11. 1/3 points | Previous Answers OSColPhys2016 28.4.WA.013.Tutorial My Notes As

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11. 1/3 points | Previous Answers OSColPhys2016 28.4.WA.013.Tutorial My Notes Ask Your Teacher Rocket A travels towards the Sun at 0.551c with respect to an observer on Earth. Rocket B travels at 0.953c with respect to rocket A in the opposite direction. (Assume rocket B travels in the +x direction.) JV rocket A Earthrocket B Sun (a) Is rocket B's speed greater in Earth's reference frame or in rocket A's reference frame? Earth's reference frame rocket A's reference frame not enough information (b) How fast (in terms of c) is rocket B traveling with respect to an observer on Earth (c) What is the length (in m) of rocket B in Earth's reference frame if rocket B has a length of 5.48 m in its own reference frame?

Explanation / Answer

(b) Velocity of rocket A in earth reference (VA) = -0.551c
-ve sign indicate that the direction is toward -x axis
Velocity of rocket B in earth reference = VB
Velocity of rocket B in rocket A reference (UB)= 0.953c
Hence the velocity of the rocket B in earth reference should be given by
VB = [(UB + VA) / 1+{(UBVA)/c2}]
VB = [(0.953 -0.551)c / 1 - {(0.953*0.551)c2/c2}]
VB = 0.8465c
(c) We know that the relativistic length is given by
L = Lo*[1-(VB/c)2]1/2
where Lo is original length = 5.48 m
L = 5.48*[1-(0.8465c/c)2]1/2
L = 2.917 m

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