Question

You are standing at $x=9.0km$and your assistant is standing at $x=3.0km.$Lightning bolt $1$strikes at $x=0km$and lightning bolt $2$strikes at $x=12.0km.$You see the flash from bolt $2$at $t=10\mu s$and the flash from bolt $1$at$t=50\mu s.$ 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

I am standing at $x=9.0km$and my assistant is standing at $x=3.0km.$

Lightning bolt $1$strikes at $x=0km$and lightning bolt $2$strikes at$x=12.0km.$

The flash from bolt $1$is at $t=50\mu s$and the flash from bolt $2$is at$t=10\mu s.$

Simply

Bolt hits away, so light takes to reach me. I see this flash at

So, the lightning hit at Light from bolt which hits away, takes to reach me.

I see it at so the lightning hit at

Bolt hits first, before bolt

Since, the assistant is in my inertial frame, she agrees that bolt hits first, before bolt