Question

1.) You are standing at x= 8.0 km and your assistant is standing at x= 5.0 km. Lightning bolt 1 strikes at x= 0 km and lightning bolt 2 strikes at x= 15 km. You see the flas from bolt 2 at t = 12 microseconds and the flash from bolt 1 at t= 52 microseconds. What is the time difference between the two?

2.) You are standing at x= 8 km. Lightning bolt 1 strikes at x= 0 km and lightning bolt 2 strikes at x= 15 km. Both flashes reach your eye at the same time. Your assistant is standing at x= 4 km. What is the difference between the two?

Answer 1

1] The light from the lightning bolt has speed c = 3 x 10⁸ m/s

distance between you and x=15km is

x' = 15-8 = 7 km = 7000 m

so, time at which the lightning strikes at x=15km is:

t = 12 x 10^-6 - (7000/3 x 10⁸) = - 11.33 x 10^-6 s

time at which it strikes at x=0 is:

t' = 52 x 10^-6 - (8000/3x10⁸) = 25.33 x 10^-6 s

the actual time difference between the two strikes is: t' - t = 36.66 x 10^-6 s

the time difference as observed by you will be 52-12 = 30 x 10^-6 s.

2]

time it takes for lightning at 2 to reach you = 23.33 x 10^-6 s

time it takes for lightning at 1 to reach you = 26.66 x 10^-6 s

so, the actual time difference between the two strikes should be 26.66 - 23.33 = 3.33 x 10^-6 s where the bolt 1 must strike first.