My point has been that the naysayers’ argument has been “no, it can’t happen, surely not, it just can’t happen, no, I don’t believe it”, whereas all the physics posted
(including kanicbird) has said that there is nothing impossible about a body hit by a 70-90mph train ending up hundreds of yards from the point of impact.
So, does anyone know how high people bounce when they hit the concrete after jumping off the Empire State building? That’d give us an idea of how elastic these collisions are.
Only on the SDMB could we turn a WAG-quote (probably from a shocked witness) about a tragic event into a physics discussion :).
Again, nothing to do with the collision in question. Hitting a concrete slab is nothing like hitting a curved aluminium panel.
Why can’t we calculate it once assuming it was a concrete slab, and once assuming it was a curved aluminum panel? Why can’t we calculate it with 100,200, and 300 yards? I don’t see the big deal with definitions. As far as decent estimations go Squinks first reply is the best I think (and surprisingly in range).
OK, how high would one bounce hitting the bottom of the bed of one of those monster open-pit mining trucks?
Maybe a squirrel dragged her. I wouldn’t put anything past a squirrel.
Little bastards.
No, it’s not a perfectly elastic collision. I was limiting my comments specifically to the notion that the woman would be thrown only the speed of the train.
In reality, this problem has a few dominant variables that have nothing to do with the basic physics of an inelastic collision. For example, we have no way of knowing how much energy would be absorbed by the deformation of the train and the body, Or at what angle the body is launched from the train. I can envision scenarios all the way from splat-and-stick up to acting like a beanbag hit by a baseball bat.
My guess is that when people saying somone was ‘thrown 100 meters from the vehicle’, it really doesn’t have anything to do with the hang time of the body, but simply the distance it was found from the point of impact.
If that body hit the ground going 70 mph, it would flip and roll a long ways down the track. So the real answer is probably that the woman hit the train, got carried some distance down track while the body stuck to the train and reacted to the impact, then got thrown back down the track, covering some distance in the air and some rolling on the ground. Add it all up, and a body could probably go a pretty good distance from the point of impact.
People (and presumably other things) hit by trains going at speed can often remain “stuck” to the front for a considerable distance, something which I doubt can be calculated mathematically.
A railway friend told me of an incident earlier this year where a bloke intent on suicide leapt in front of an early-morning Midland Main Line train a few miles north of Bedford station. The body - well, most of it, anyway - was still on the train as it came into the station, much to the consternation of the passengers waiting to board it.
But this is rather different from the incident at Elsenham, where the two unfortunate girls were at track level: the driver in my anecdote later said that the bloke had jumped up and out at him, which meant that he impacted with the train rather higher up. I am not sure whether it was the same type of train as at Elsenham or a HST.
Hmmmm, saw a Class 170 crossing a bridge over the A14 in front of me this morning, doing somewhere over 70mph - I had no difficulty picturing a body being flung a significant distance by it.
I’m a little out of my league mathematically here, but…
Based on an article s/he read, the OP posed this factual question:
“How fast would a train have to be moving to throw [a 100 lbs girl] 200 yards?”
I’m really curious about the physics involved here. So maybe a few standards are needed here (for my understanding).
Definition of thrown: Distance from the point of impact to the final resting place. This would include the ‘sticking’ time, the actual thrown distance in the air and the rolling or bouncing distance (and squirrel dragging).
So, is this:
Omniscient: “m1v1i + m2v2i = m1v1f + m2v2f”
…correct, or is this?:
kanicbird: "Sorry to brake it to ya, but it is true when the mass of one object is very large to that of the other (technically it approaches 2x). It is the same of bouncing a superball against a wall, the superballs velocity is the same but in the opposite direction.
Ball moving at the wall at 70mpg, leaving at -70mph is the same as the ball at 0 mpg, wall at -70mph, and after the ball will be moving at -140mph."
I realize that there are things that can’t be accounted for, but let’s leave out whether the reporters comments can be taken at face value.
Sorry if the morbidity of this subject over-runs the the science value.
They both are, but the 1st one can’t be used because we don’t know about the loss of speed of the train. Actually I think if you take the limit as m2 goes to infinity you will find that both equations are the same.
They both are, but the 1st one can’t be used because we don’t know about the loss of speed of the train. Actually I think if you take the limit as m2 goes to infinity you will find that both are the same. (though it may be the Ke energy equations, which are derived from momentum anyway)
According to this site the low altitude terminal velocity of a human body falling under the force of gravity is 117-125 mph. I’m not sure how the impulse from a train would compare, but I suspect that in the absence of a continuing push the body would slow rapidly to that figure and would of course continue to slow down during the whole time.
With a starting velocity of 125 mph and launched at a 10[sup]o[/sup] angle up with no air resistance a body will travel 120 yards and be in the air for 2 seconds.
That doesn’t work. Terminal velocity applies when the body is falling from a great height, not being hit by a train.
I don’t agree. Terminal velocity is a result of air resistance and if a body starts out through the air at a velocity higher than that as the result of an impulse it will quickly slow to that velocity regardless of the direction in which it is traveling.
Wrong.
“Terminal velocity” only has meaning with regard to air resistance versus the force of gravity and is defined as:
It has nothing whatsoever to do with a body flying through the air propelled by anything other than gravity.
Heh! 
Actually, it does have something to do with it. If the body’s initial velocity after the impact was over the terminal velocity and the direction was perpendicular to gravity or some degree against it (which is almost certain if she bounced so far), the body would necessarily have been decelerating at over 9.8 m/s^2. You can brush off speed fairly quickly at that rate of deceleration, but I don’t think it would affect the results by any order of magnitude.
Right. The terminal velocity in free fall gives us a chance to make a ballpark estimate as to the maximum distance a body would travel.
When a falling body reaches terminal velocity at relatively low altitude the drag is equal to the weight of the body and thus would produce the same acceleration opposite the direction of motion as gravity produces downward. Various sources give the terminal velocity for various aspects as around 125 mph. Drag force is proportional to the square of the velocity so we can say that at any velocity, v, the acceleration opposite the direction of motion is 32.17*(v/125)[sup]2[/sup] where v is in mph and 32.17 is the acceleration of gravity in English units.
Here are graphs of the trajectory and velocity of a perfectly elastic body struck by a train traveling at 70 mph. I assumed the body’s initial velocity after impact to be 140 mph launched at a 15[sup]o[/sup] angle up.
The maximum distance the body would travel through the air is a little over 90 yards. Add and additional 30 yards of roll. And this is for an elastic collision. A human body and a train would be far from elastic.