3. The Federation space cruiser Execrable is floating in Federation territory at rest relative to the bor-der of Klingon space, which is 6.00 min away in the +x direction. Suddenly, a Klingon warship fliespast the cruiser in the direction of the border at a speed of B 3/5. Call this event A, and let it de-fine time zero in both the Klingon and cruiser reference frames. At ig = 5.00 min according to thecruiser clocks, the Klingons emit a parting disrupter blast (event B) that travels at the speed of lightback to the cruiser. The disrupter blast hits the cruiser and disables it (event C), and a bit later (ac-cording to cruiser radar measurements) the Klingons cross the border into Klingon territory (eventD).(a) Draw a two-observer spacetime diagram of the situation, taking the cruiser to define theHome Frame and the Klingon warship to define the Other Frame. Draw and label the worldlines of the cruiser, the Klingon territory boundary, the Klingon warship, and the disruptorblast. Draw and label events A, B, C, and D as points on your diagram(b) When does the disruptor blast hit, and when do the Klingons pass into their own territoryaccording to clocks in the cruiser's frame? Answer by readingthe times of these events directlyfrom the diagram.(c) The Klingon-Federation Treaty states that it is illegal for a Klingon ship in Federation territoryto damage Federation property. When the case comes up in interstellar court, the Klingonsclaim that they are within the letter of the law: according to measurements made in their ref-erence frame, the damage to the Execrable occurred after they had crossed back into Klingonterritory: thus they were not in Federation territory at the time. Did event C (disruptor blasthits Execrable) really happen after event D (Klingons cross border) in the Klingons' frame?Answer this question by using your two-observer diagram.(d) Verify your answers above using the appropriate transformation equations

Question
Asked Nov 25, 2019
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3. The Federation space cruiser Execrable is floating in Federation territory at rest relative to the bor-
der of Klingon space, which is 6.00 min away in the +x direction. Suddenly, a Klingon warship flies
past the cruiser in the direction of the border at a speed of B 3/5. Call this event A, and let it de-
fine time zero in both the Klingon and cruiser reference frames. At ig = 5.00 min according to the
cruiser clocks, the Klingons emit a parting disrupter blast (event B) that travels at the speed of light
back to the cruiser. The disrupter blast hits the cruiser and disables it (event C), and a bit later (ac-
cording to cruiser radar measurements) the Klingons cross the border into Klingon territory (event
D).
(a) Draw a two-observer spacetime diagram of the situation, taking the cruiser to define the
Home Frame and the Klingon warship to define the Other Frame. Draw and label the world
lines of the cruiser, the Klingon territory boundary, the Klingon warship, and the disruptor
blast. Draw and label events A, B, C, and D as points on your diagram
(b) When does the disruptor blast hit, and when do the Klingons pass into their own territory
according to clocks in the cruiser's frame? Answer by readingthe times of these events directly
from the diagram.
(c) The Klingon-Federation Treaty states that it is illegal for a Klingon ship in Federation territory
to damage Federation property. When the case comes up in interstellar court, the Klingons
claim that they are within the letter of the law: according to measurements made in their ref-
erence frame, the damage to the Execrable occurred after they had crossed back into Klingon
territory: thus they were not in Federation territory at the time. Did event C (disruptor blast
hits Execrable) really happen after event D (Klingons cross border) in the Klingons' frame?
Answer this question by using your two-observer diagram.
(d) Verify your answers above using the appropriate transformation equations
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3. The Federation space cruiser Execrable is floating in Federation territory at rest relative to the bor- der of Klingon space, which is 6.00 min away in the +x direction. Suddenly, a Klingon warship flies past the cruiser in the direction of the border at a speed of B 3/5. Call this event A, and let it de- fine time zero in both the Klingon and cruiser reference frames. At ig = 5.00 min according to the cruiser clocks, the Klingons emit a parting disrupter blast (event B) that travels at the speed of light back to the cruiser. The disrupter blast hits the cruiser and disables it (event C), and a bit later (ac- cording to cruiser radar measurements) the Klingons cross the border into Klingon territory (event D). (a) Draw a two-observer spacetime diagram of the situation, taking the cruiser to define the Home Frame and the Klingon warship to define the Other Frame. Draw and label the world lines of the cruiser, the Klingon territory boundary, the Klingon warship, and the disruptor blast. Draw and label events A, B, C, and D as points on your diagram (b) When does the disruptor blast hit, and when do the Klingons pass into their own territory according to clocks in the cruiser's frame? Answer by readingthe times of these events directly from the diagram. (c) The Klingon-Federation Treaty states that it is illegal for a Klingon ship in Federation territory to damage Federation property. When the case comes up in interstellar court, the Klingons claim that they are within the letter of the law: according to measurements made in their ref- erence frame, the damage to the Execrable occurred after they had crossed back into Klingon territory: thus they were not in Federation territory at the time. Did event C (disruptor blast hits Execrable) really happen after event D (Klingons cross border) in the Klingons' frame? Answer this question by using your two-observer diagram. (d) Verify your answers above using the appropriate transformation equations

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Expert Answer

Step 1

a)

The worldline diagram for the given problem is given below ,

 

World line of
Klingon tew t
Boundoay
World Line
of cruisu
6+
Norld
ine of
Waschip
3 +
A
지ㅇ
7
World Line of
distupter blast
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World line of Klingon tew t Boundoay World Line of cruisu 6+ Norld ine of Waschip 3 + A 지ㅇ 7 World Line of distupter blast

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Step 2

b)

From the world line diagram in step 1, from the cruiser’s frame of reference,

1) The disrupter blast hits the cruiser (event  C) at t = 8 sec

2) The Klingons  pass into their own territory (event D) at t = 10 sec.

 

Step 3

c)

Use the Lorentz’s Transformation equations as follows,

Let (x , t) denote the position and time coordinates in the frame of reference of the cruiser,

Let (x’, t’) denote the position and time coordinates in the reference frame of the Klingon warship.

Let v be the velocity of the Klingon warship as seen from the cruiser’s frame of reference

The Lorentz transformatio...

(Xefc)=(0,8)
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(Xefc)=(0,8)

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