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crimsonidol
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Homework Statement
A stellar object at some known large distance ejects a ‘jet’ at speed v towards
an observer obliquely, making an angle θ with the line of sight. To the observer the
jet appears to be ejected sideways at speed V . Prove V = c sin θ (c/v − cos θ )−1 , and
show that this can exceed c, for example, when θ = 45◦ . [Indeed, such apparently
superluminal jets once had observers worried—briefly.]
Question from Rindler 2.21
Homework Equations
Nothing more is supplied in the question.
The Attempt at a Solution
I have tried to use the velocity transformation in the frame of stellar object?(Say frame S). Since I know the speed of the object in observers frame(say S') which is V in the y direction and velocity u'(0,V,0) say in standart configuration.and I know the vcosθ is the speed in x direction vsinθ is the speed in y direction and velocity u(vcosθ,vsinθ,0) in the frame S. However I do not know the observer's relative speed in stellar object's frame.
I tried to find by applying velocity transformation in x direction first to find relative speed of observer and then applied in y direction but no use. I have found out to satisfy the given equation speed of the observer should be c relative to the stellar object. What do I miss? I think I'm missing something silly but I cannot find out. I have been thinking for days. Please give me clue.