At 11h 0m 0.0000s AM a boiler explodes in the basement of the Denver Science Museum. At 11h 0m 0.0003s, a similar boiler explodes in the basement of a ski lodge in Aspen at a distance of 150 km from the first explosion. Show that in the reference frame of a spaceship moving at a speed greater than v=0.6c from Denver to Aspen, the first explosion occurs after the second.
x=[itex]\gamma[/itex](x' + vt')
t=[itex]\gamma[/itex](t' + vx'/c^2)
Δt = [itex]\gamma[/itex]vL/c^2
time and length dilation
The Attempt at a Solution
I first state that from the ship's perspective, the two boilers are moving, the one in denver away from the ship at 0.6c, the one in aspen towards the ship at 0.6c. I can find that, due to time dilation, the actual time between explosions as viewed from the ship would be 0.00024s, but dont know where to go from there. Also I used the simultaneity equation using Δt=0.0003s to find the distance between the two blasts, which was just length dilation in the end so i did more work for nothing. Im stumped now though. I have both dilated time and length of travel, but how can i show that the explosion in aspen happens first?