A rocket moves with a velocity of 0.854 c to the right with respect to a station

Question

A rocket moves with a velocity of 0.854c to the right with respect to a stationary observer A. An observer B moving relative to observer A finds that the rocket is moving with a velocity of 0.928c to the left. What is the velocity of observer B relative to observer A? (Hint: Consider observer B's velocity in the frame of reference of the rocket. Give your answer to three significant figures. Let the positive direction be to the right. Indicate the direction with the sign of your answer.)

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Explanation / Answer

Velocity of observer B relative to observer A is

u ' = u + v / 1 + ( u v / c^2 )

u'( 1 + u v / c^2 ) = u + v

u ' + u u' v / c^2 = u v

v = u ' - u / 1 - ( u u ' / c^2 )

= ( 0.928 c - 0.854 c ) / 1 - [ (0.928c)(0.854c)/ c^2 ]

= 0.35c

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