Answer
(a) Since a signal could reach $x = 1200~m$ before $6.0~\mu s$, it is possible that event A caused event B.
(b) Since a signal could not reach $x = 2400~m$ before $8.0~\mu s$, it is not possible that event A caused event C.
Work Step by Step
(a) We can find the time required for a signal traveling at the speed of light to travel from $~x = 300~m~$ to $~x = 1200~m$:
$t = \frac{d}{c}$
$t = \frac{1200~m-300~m}{3.0\times 10^8~m/s}$
$t = \frac{900~m}{3.0\times 10^8~m/s}$
$t = 3.0\times 10^{-6}~s$
$t = 3.0~\mu s$
We can find the earliest time a signal could reach $x = 1200~m$:
$t = 2.0~\mu~s+3.0~\mu s = 5.0~\mu s$
Since a signal could reach $x = 1200~m$ before $6.0~\mu s$, it is possible that event A caused event B.
(b) We can find the time required for a signal traveling at the speed of light to travel from $~x = 300~m~$ to $~x = 2400~m$:
$t = \frac{d}{c}$
$t = \frac{2400~m-300~m}{3.0\times 10^8~m/s}$
$t = \frac{2100~m}{3.0\times 10^8~m/s}$
$t = 7.0\times 10^{-6}~s$
$t = 7.0~\mu s$
We can find the earliest time a signal could reach $x = 2400~m$:
$t = 2.0~\mu~s+7.0~\mu s = 9.0~\mu s$
Since a signal could not reach $x = 2400~m$ before $8.0~\mu s$, it is not possible that event A caused event C.
