Question

You are standing at $x=9.0km$and your assistant is standing a $x=3.0km$Lightning bolt $1$strikes at$x=0km$and a lightning bolt $2$strikes at$x=12.0km$. You see the flash from bolt $2$at$t=10ms$and the flash from bolt$1att=50ms$ According to your assistant, were the lightning strikes simultaneous? If not, which occurred first, and what was the time difference between the two?

Short answer

The assistant is in my inertial frame , she agrees that bolt $2$hits first ,$20\mu s$ before bolt $1$.

Step-by-step solution

Given Information 

We have given you are standing at$x=9.0km$, your assistant is standing at $x=3.0km$, Lightning bolt $1$strikes at$x=0km$ , the flash from bolt$2$at$t=10ms$.

Explanation 

The bolt $1$hits $9km$away, then the light takes $30\mu s$to reach me. I see this flash at $t=50\mu$.

Therefore, the lighting hit at $t_1=20\mu s$. Light from the bolt $2$, which hits $3km$away, takes to reach me.

I see it at $10\mu s$, so the lighting hit at role="math" localid="1650112197207" $t_2=0\mu s$.

Bolt $2$hits first $20\mu s$ before bolt $1$.

Hence, the assistant is in my interial frame , she agrees that bolt $2$hits first,$20\mu s$ before bolt$1$.