A light flash leaves a master clock at $x=0$ at time $t=-12 \mathrm{~s}$, is reflected from an object a certain distance in the $-x$ direction from the origin, and then returns to the origin at $t=+8 \mathrm{~s}$. From this information, we can infer that the spacetime coordinates of the reflection event are $[t, x]=$
A) $[4 \mathrm{~s}, 20 \mathrm{~s}]$
B) $[-4 s,-20 s]$
C) $[10 \mathrm{~s},-2 \mathrm{~s}]$
D) $[2 \mathrm{~s},-10 \mathrm{~s}]$
E) $[-2 s,-10 s]$
F) Other (specify)

Question

Quizplus · Accepted Answer

The total round trip time for the light flash is $8 - (-12) = 20$ seconds. Since light takes the same time to travel to the object and back, it takes $20 / 2 = 10$ seconds each way. The reflection event happens $12 + 10 = 22$ seconds after the initial time, placing it at $t = -2$ seconds. Given that light travels at a constant speed (assuming $c = 1$ unit distance per unit time for simplicity), the distance to the object and back is $20$ units, so the object is $10$ units away in the $-x$ direction. Therefore, the spacetime coordinates of the reflection event are $[-2 s, -10 s]$.

A Light Flash Leaves a Master Clock At x=0x=0x=0 At Time t=−12 st=-12 \mathrm{~s}t=−12 s

A Light Flash Leaves a Master Clock At $x=0$ At Time $t=-12 \mathrm{~s}$