Velocity addition I: Suppose you are a far-future asteroid miner. The asteroid is seeded
with explosives such that, at a given time, an explosive breaks the asteroid in two pieces,
sending one half with ux = +0.8c and the other half with ux = −0.8c relative to the aster-
oid’s rest frame. At a later time, each half is broken in two, sending each half with \pm 0.8c
in the x−direction relative to the piece’s new rest frame. At a later time, there is a third
explosion, again sending each half out at \pm 0.8c in the x− direction.
(a) Classically, how fast is the right-most piece moving relative to the original asteroid’s
rest frame after three explosions? the left-most piece?
(b) Relativistically, how fast is the right-most piece moving relative to the original rest
frame after three explosions?
(c) Relativistically, how fast is the left-most piece moving relative to the right-most piece
after three explosions?