The truck was coming from the direction the camera was pointing, and the gate on that ("near") side of the track was mounted on that signal/gate pylon on the right. (You can actually see the gate being test-operated in the video...)
The train was traveling from right to left from that viewpoint -- and it came to a stop with the rear unit right at the crossing/point of collision.
The truck cab/chassis was knocked backward and almost across the width of the road's pavement (not very far...).
IF the gate was, indeed, down before the truck moved onto the track, the truck would have had to go around the gate arm on its "free" left end -- and, then turn (right) in the direction of the train to go (left) around the end of the gate on the opposite side of the track.
In order to go around the far end of the other gate, the truck would have had to drive "up" the track (in the direction of the oncoming train for at least the length of the crossing arms (full left-right width of the crossing).
That would have placed the two vehicles in a near-head-on collision position -- with damage all across the front of the train engine.
BUT -- the collision damage on the train engine was on the left front corner, and the collision point on the truck was its right front corner.
Now comes the "fun part": '-)
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Notice that, in the video, the gate on the truck's approach side of the crossing was not only functional, post collision -- the wooden gate arm was still whole and unbroken! Still post-collision photos show both gate arms down -- and intact.
IF that gate was down during the collision -- why wasn't it smashed to splinters as the truck came flying back through it?
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Look closely -- right along the top of the ambulance on the far side -- and along the road centerline: that wooden gate arm is down -- and undamaged!
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Per Occam's Razor, the simplest, most likely answer is: That "near" gate was in the "UP" position when the collision occurred!
Also, facebook comments by "locals" claimed that that the gate(s) at that crossing had been operating "erratically" for some time...
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More to come...
My understanding is that the 1st train pic in your post is not from that accident but another just used in the news coverage for some reason.
Just look at the paint striping on the 2 trains- they are different
I find it highly unlikely that the left side of that engine has a paint scheme entirely mismatched to the right side. . . especially when the nose has the red, white, and blue bands centered and looking as if they are repeating on both sides.
A little research on Amtrak livery gives the answer: Amtrak engines are always painted symmetrically on both sides. The livery in the bottom photo is called "Chevron 7" and is in the process of being phased out. It is primarily being used for commuter trains of a different type than this train.
I think that is a replacement engine brought in to move this train to its destination after the "Flag Phase III" motif livery damaged engine we see in the top photo was removed as unserviceable.
The photo showing the engine in the bottom was taken hours later. The state of the crossing gate in this photo at this time cannot be dispositive of its State after the accident; they were already making repairs to the crossing in preparation to reopening the line and moving that minimally damaged train out of there. Nor do we, at this time, know how far the engine has moved the train itself in the process of removing the damaged engine or hooking up its replacement, These facts are unknown. However, looking at the top photo with what appears to be the damaged engine still connected to the passenger cars, I do not see the crossing at all. From that, we know the train was moved quite a bit before the second photo was taken.
Read the NTSB prelim report, it describes a lot of details you appear to be struggling with.
The train struck the left rear of the truck which damaged the left front of the locomotive.
It states the forward facing train camera shows both crossing arms were down.
It also states there were two locomotives on the train and it's clear from the photos it was push/pull, not double-heading.
I think the sudden and violent counterclockwise rotational thrust of the truck body killed the far right truck passenger as the cab would have literally smashed into him even though the cab was not struck directly.