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https://texercises.com/exercise/overtaking-spaceships/
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Exercise:
An old spaceship is overtaken by a more modern one. In the reference frame of the slower spaceship the faster one flies with beiO while an outside observer measures a velocity of beoO for the faster spaceship. Calculate the velocity of the slower spaceship in the reference frame of the outside observer.

Solution:
The two reference frames are the outside observer O and the slower spaceship O'. The velocity of the faster spaceship is u'beiO in the frame O' and ubeoO in the frame O. The velocity of the slower spaceship relative to the outside observer is v. vspacemm Solving the formula for the addition of relativistic velocities u fracv+u'+fracvu'c^ for v yields uc^+uvu' vc^+u'c^ Longrightarrow v c^-u u' u-u'c^ Longrightarrow v fracu-u' c^c^-u u' vF fracbeo-bei-fracbeotimesbeic^ resultvP
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Exercise:
An old spaceship is overtaken by a more modern one. In the reference frame of the slower spaceship the faster one flies with beiO while an outside observer measures a velocity of beoO for the faster spaceship. Calculate the velocity of the slower spaceship in the reference frame of the outside observer.

Solution:
The two reference frames are the outside observer O and the slower spaceship O'. The velocity of the faster spaceship is u'beiO in the frame O' and ubeoO in the frame O. The velocity of the slower spaceship relative to the outside observer is v. vspacemm Solving the formula for the addition of relativistic velocities u fracv+u'+fracvu'c^ for v yields uc^+uvu' vc^+u'c^ Longrightarrow v c^-u u' u-u'c^ Longrightarrow v fracu-u' c^c^-u u' vF fracbeo-bei-fracbeotimesbeic^ resultvP
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special relativity
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velocity addition
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