a 100 sec long train (as measured at rest) moves in the x-direction with speed B=4/5 . at the instant the rear of the train passes a post on the ground , everyone sets their clocks to zero. at this "same" time , an observer on the train at the front turns on a light and an observer at the rear turns on a light. so, these lights are turned on simultaneously in the train's frame.

a) at what time is the rear light turned on according to an observer on the ground at the post?

b) at what time is the front light turned on according to an observer on the ground at the post?

c) what is the position of the front of the train when the rear light is turned on, according to an observer on the ground?

d) what is the position of the rear of the train when the front light is turned on, according to an observer on the ground?

e) when does the light from the front light reach an observer on the ground at the post?