# "One of the girls was thrown hundreds of yards by the impact of the train."
**URL:** https://boards.straightdope.com/t/one-of-the-girls-was-thrown-hundreds-of-yards-by-the-impact-of-the-train/333975
**Category:** Factual Questions
**Created:** [December 4, 2005, 2:49am UTC](https://boards.straightdope.com/t/one-of-the-girls-was-thrown-hundreds-of-yards-by-the-impact-of-the-train/333975 "2005-12-04T02:49:28Z")
**Posts on this page:** 3
**Page:** 4
### Author:  [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)
#### Post date: [January 7, 2006, 5:01am UTC](https://boards.straightdope.com/t/one-of-the-girls-was-thrown-hundreds-of-yards-by-the-impact-of-the-train/333975/61 "2006-01-07T05:01:20Z")
> [@snailboy](#):
>
> 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 at low altitude 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](http://pg.photos.yahoo.com/ph/dwsimm2000/detail?.dir=/8cf7&.dnm=aac3.jpg&.src=ph) 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. Note that the vertical scale on the velocity graph is wrong. The velocities are in mph and not ft/sec.
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.
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### Author:  [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)
#### Post date: [January 7, 2006, 5:03am UTC](https://boards.straightdope.com/t/one-of-the-girls-was-thrown-hundreds-of-yards-by-the-impact-of-the-train/333975/62 "2006-01-07T05:03:01Z")
Sorry for the double post.
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### Author:  [@Scupper](https://boards.straightdope.com/u/Scupper)
#### Post date: [January 9, 2006, 4:14pm UTC](https://boards.straightdope.com/t/one-of-the-girls-was-thrown-hundreds-of-yards-by-the-impact-of-the-train/333975/63 "2006-01-09T16:14:37Z")
The air resistance of a human body is germane to the problem and that **can** be reverse-inferred from terminal velocity. My bad.
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