Frame is the rest frame of an asteroid-mining base

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics

Relativity and Gravitation, Ch The postulates and the Lorentz transformation

Problem

Frame

S

is the rest frame of an asteroid-mining base. Frame

S'

is the rest frame of a shuttle moving at

v = 0.500c

along the common

+x

axis of

S

; the axes are parallel and the origins coincide at

t = t' = 0

. Both frames are inertial. Take

c = 2.998\times10^{8}\ \mathrm{m\,s^{-1}}

. ((a)) A small rock strikes the shuttle's hull, making a flash that the shuttle's crew record at

x' = 150\ \mathrm{m}

y' = 40.0\ \mathrm{m}

t' = 0.500\ \mu\mathrm{s}

S'

. Find the coordinates

x

y

and

t

of this event in the base frame

S

. ((b)) A cargo pod moves along the

x'

axis at

0.300c

in the

-x'

direction, as measured in

S'

. Find its velocity in

S

, as a multiple of

c

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