Question

You are standing at $x=9.0km.$Lightning bolt $1$strikes at $x=0km$and lightning bolt $2$strikes at $x=12.0km.$ Both flashes reach your eye at the same time. Your assistant is standing at $x=3.0km.$ Does your assistant see the flashes at the same time? If not, which does she see first, and what is the time difference between the two?

Short answer

The difference is$40\mu s.$

Step-by-step solution

Given Information

We have given that,

I am standing at $x=9.0km$

Lightning bolt $1$strikes at $x=0km$and lightning bolt $2$strikes at $x=12.0km.$Both flashes reach my eye at the same time.

My assistant is standing at $x=3.0km.$

Simplify

Bolt $1$is $9.0km$away, thus the light take $30mus$to reach me. Bolt $2$is $3.0km$away, thus it will take $10\mu s$to reach me.

Because both flashes hit my eye at the same moment, the occurrence took $20\mu s.$

It takes light from bolt $110\mu s$to reach my assistance and light from bolt $230\mu s$to reach my assistance.

So, she sees the flash from bolt $1$at $t=10\mu s$and flash from bolt $2$at localid="1649506376024" $t=50\mu s.$

So, the difference is $40\mu s.$