Train frame $$S is moving at speed v $=0\mathrm{.}7$c relative to ground frame S$.$ The origins of the

two frames coincide at t $=$t $=0.$ An observer at the origin in the ground frame sends a

light pulse to ground$-$based Mary at position $$x$,$ y$,$ z$=2,3,1($in meters$).$

$($a$)$ How much time elapses in the ground frame before the light pulse is received by Mary?

$($b$)$ How much time elapses in the train frame before the light pulse is received by Mary?

$($c$)$ At what train$-$frame position $$x$,$y$,$z$$ is Mary when she receives the light pulse?

$($d$)$ How much time would it take for a light pulse in the train frame to move from its origin

to position $$x$,$y$,$z$?$ Check: you should get the same answer as in part $($b$)$