Question $2$

Two inertial frames $S$ and $S^{\text{'}}$ are in the standard configuration. As measured in the $S$ frame, $S^{\text{'}}$ has velocity $V=0\mathrm{.}8c$ along the positive $x-$axis. An observer that is stationary in the $S^{\text{'}}$ frame reports that two events $($A and B$)$ occur at the same place at $x_A^{\text{'}}=x_B^{\text{'}}=250m.$ The observer also meaures the time of Event $A$ to be $t_A^{\text{'}}=1{10}^{-8}s$ and Event $B$ as $t_B^{\text{'}}=7{10}^{-8}s.$

$($a$)$ What is the time of Event B$,$ as measured in $S?$

$12$

$($b$)$ Calculate the spacetime separation between the events.

$|10|$

$($c$)$ The observer in $S$ claims that Event A may have caused Event B$,$ but the observer in $S^{\text{'}}$ says that is physically impossible. Who is correct and why?

$[4]$

$($d$)$ Draw a rough Minkowski diagram to indicate these two events in both the $S$ and $S^{\text{'}}$ frame.

$6$

$1$