odiousgambit
Joined: Nov 9, 2009
• Posts: 8339
July 12th, 2011 at 9:20:23 AM permalink
Have a bet going about how fast the poor guy was going in TX who fell out of the stands catching a ball and got killed. He fell 20 ft as I remember, we are using that anyway.

A discussion came up about how fast he was going when he hit the concrete. He died from something that happened in his chest, torn aorta or something, not head injury so we were talking about how hard he hit.

Working with 32 ft/ sec^2 I get the algebraic formula x*t / 2 = distance, where x= 32 ft per second square, and t = time. Whipping the algebra around I get 20 feet fallen equals 1.25 seconds, then I take that figure and use it to get 40 ft per second terminal velocity ,which is approximately 26 to 27 mph I hope. He is saying online calculators I havent seen are giving a different answer, and I am betting him he is using them wrong.

['in a vaccuum' factor disregarded]

Coming up with the formula I got is Calculus in reality, I think, to take a constant, multiply times something else to get one answer, and divide it by 2 for the next answer? I actually remember how to do it sort of tedious step by step though.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
ItsCalledSoccer
Joined: Aug 30, 2010
• Posts: 735
July 12th, 2011 at 9:49:37 AM permalink
Unless I'm missing something, it seems like a basic kinematics system. The two equations to be solved are:

1) v = gt, and

2) d = 0.5 g t^2

assuming, of course, a = g and v0 = 0. So with d = 20 ft, I get ...

t = v/g

20 = 0.5 v^2 / g ; v = 35.9 ft/s = 24.5 MPH

t = v/g = 1.11 s

So, I guess it would be like wrecking your car at 25 MPH against something that doesn't move when you hit it.
FleaStiff
Joined: Oct 19, 2009
• Posts: 14460
July 12th, 2011 at 9:51:01 AM permalink
Angular momentum?
He may have hit his head but the body then toppled and the internal stress can be measured as "sufficient".
ItsCalledSoccer
Joined: Aug 30, 2010
• Posts: 735
July 12th, 2011 at 9:52:42 AM permalink
Quote: FleaStiff

Angular momentum?
He may have hit his head but the body then toppled and the internal stress can be measured as "sufficient".

No doubt there's more to it than my equations say; it wasn't a rigid-body situation. So there's a lot more to account for than just the kinematics.

But still ... youch. Not a fun thing.
odiousgambit
Joined: Nov 9, 2009
• Posts: 8339
July 12th, 2011 at 10:04:52 AM permalink
Quote: ItsCalledSoccer

assuming, of course, a = g

I may have lost my bet. To start, what does this mean? I see "a" nowhere else
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
matilda
Joined: Feb 4, 2010
• Posts: 317
July 12th, 2011 at 10:18:40 AM permalink
a = acceleration.
odiousgambit
Joined: Nov 9, 2009
• Posts: 8339
July 12th, 2011 at 10:20:25 AM permalink
possibly answering my own question, acceleration equals force of one G? of course!

I lost my bet. The formula is X*t^2 / 2= distance. I was not squaring the time in seconds.

PS: what about calculus? Aren't these calculations what got Newton to invent calculus?
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
ItsCalledSoccer
Joined: Aug 30, 2010
• Posts: 735
July 12th, 2011 at 10:30:06 AM permalink
Quote: odiousgambit

PS: what about calculus. Aren't these calculations what got Newton to invent calculus?

As best I understand it ... kind of. Newton and Liebnitz essentially invented calculus at about the same time on separate paths, but Newton generally gets credit. Differential and integral calculus make describing and solving Newton's equations easier, and elemental analysis has become a standard way of approaching a problem in a lot of scientific fields, almost to a fault. But in the end, integral calculus is essentially adding tiny rectangles/trapezoids, and differential calculus is calculating the slope on line segments. You can see, in the description of gravity, etc., and motion, etc., that a shorthand way to do this would be handy. And for scientific rigor, an exact calculation also serves the overall betterment.

IIRC, I think calculators use algorithms like those to calculate differentials or integrals, and you can set the accuracy on them to whatever you want ... although calculators are so much better now than the first "calculus" calculators that that may not be the case any more.
Ayecarumba
Joined: Nov 17, 2009
• Posts: 6763
July 12th, 2011 at 10:58:21 AM permalink
FWIW, the unfortunate guy hit a crossbar on his way down. This trauma is probably where the torn aorta came from, not from the impact on the concrete below.
Simplicity is the ultimate sophistication - Leonardo da Vinci
DJTeddyBear
Joined: Nov 2, 2009