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Spaceship A passes earth at speed V when its clock (as well as the adjacent
earth clock) reads zero (event £1). When the earth clock reads T, spaceship B passes
earth, moving at speed U in the same direction as the first (event £2). Assume
that U> V; let 5 be the earth frame and S' be the rest frame of ship A. Eventually,
ship B catches up to A (event £3). Note the similarity between this problem and
problem 3.10.
(a) Find the time of £3 in frame S.
(b) Find the time of E2 in frame 5'.
(c) Find the time of £3 in frame 5'.
(d) According to 5' observers, how far away was earth at £2?
(e) From these results, find the velocity of ship B as measured by observers on
A. This is the relativistic velocity transformation law, which will be derived from
the Lorentz transformation in the next chapter (eq. [4.15]).
![3.11. Spaceship A passes earth at speed V when its clock (as well as the adjacent
earth clock) reads zero (event E,). When the earth clock reads T, spaceship B passes
earth, moving at speed U in the same direction as the first (event E,). Assume
that U>V; let S be the earth frame and S' be the rest frame of ship A. Eventually,
ship B catches up to A (event E3). Note the similarity between this problem and
problem 3.10.
(a) Find the time of Ez in frame S.
(b) Find the time of Ez in frame S'.
(c) Find the time of Ez in frame S'.
(d) According to S' observers, how far away was earth at E,?
(e) From these results, find the velocity of ship B as measured by observers on
A. This is the relativistic velocity transformation law, which will be derived from
the Lorentz transformation in the next chapter (eq. [4.15]).](https://content.bartleby.com/qna-images/question/586dedfb-b3a5-42ce-892d-f1e509100719/4444eec1-1f65-4257-8255-e4b797a6e51a/mdzmiv4_processed.png)
Transcribed Image Text:3.11. Spaceship A passes earth at speed V when its clock (as well as the adjacent
earth clock) reads zero (event E,). When the earth clock reads T, spaceship B passes
earth, moving at speed U in the same direction as the first (event E,). Assume
that U>V; let S be the earth frame and S' be the rest frame of ship A. Eventually,
ship B catches up to A (event E3). Note the similarity between this problem and
problem 3.10.
(a) Find the time of Ez in frame S.
(b) Find the time of Ez in frame S'.
(c) Find the time of Ez in frame S'.
(d) According to S' observers, how far away was earth at E,?
(e) From these results, find the velocity of ship B as measured by observers on
A. This is the relativistic velocity transformation law, which will be derived from
the Lorentz transformation in the next chapter (eq. [4.15]).
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