Calculus Bet On the Line!
July 12th, 2011 at 9:20:23 AM
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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.
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
July 12th, 2011 at 9:49:37 AM
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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.
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.
July 12th, 2011 at 9:51:01 AM
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Angular momentum?
He may have hit his head but the body then toppled and the internal stress can be measured as "sufficient".
He may have hit his head but the body then toppled and the internal stress can be measured as "sufficient".
July 12th, 2011 at 9:52:42 AM
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Quote: FleaStiffAngular 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.
July 12th, 2011 at 10:04:52 AM
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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
July 12th, 2011 at 10:18:40 AM
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a = acceleration.
July 12th, 2011 at 10:20:25 AM
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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?
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
July 12th, 2011 at 10:30:06 AM
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Quote: odiousgambitPS: 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.
July 12th, 2011 at 10:58:21 AM
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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
July 12th, 2011 at 11:05:36 AM
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Am I the only one here who thinks that the subject matter of this bet is just a tad, oh I don't know..., Icky?
If so, then I'll just say that hitting that crossbar would have affected his speed and acceleration.
If so, then I'll just say that hitting that crossbar would have affected his speed and acceleration.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
July 12th, 2011 at 11:11:10 AM
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Quote: DJTeddyBearAm I the only one here who thinks that the subject matter of this bet is just a tad, oh I don't know..., Icky?
If so, then I'll just say that hitting that crossbar would have affected his speed and acceleration.
No, DJ, you're not the only one. Not so much the discussion for me, but the existence of a wager. Sorta like the Romans tossing dice for Jesus' garments at the Crucifixion.
Simplicity is the ultimate sophistication - Leonardo da Vinci
July 12th, 2011 at 11:17:51 AM
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Quote: DJTeddyBearAm I the only one here who thinks that the subject matter of this bet is just a tad, oh I don't know..., Icky?
Morbid, too. And not very tactful.
Donald Trump is a fucking criminal
July 12th, 2011 at 2:07:13 PM
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Quote: DJTeddyBearAm I the only one here who thinks that the subject matter of this bet is just a tad, oh I don't know..., Icky?
Quote: AyecarumbaNo, DJ, you're not the only one. Not so much the discussion for me, but the existence of a wager. Sorta like the Romans tossing dice for Jesus' garments at the Crucifixion.
Quote: NareedMorbid, too. And not very tactful.
Wow. Ouch. Sorry.
Honestly, if it wasn't all three of you noticing... well, I had almost no trepidation about posting about this, not to say I didnt thing the whole business was awful. I guess someone needed to point this out.
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
July 14th, 2011 at 7:34:00 AM
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Quote: ItsCalledSoccert = v/g = 1.11.
I agree, but I get the answer a different way.
First, let's use 32.2 feet per second per second as the rate of acceleration.
Take the integral of acceleration to get velocity: v=32.2 t+c. We know velocity must be 0 at time 0, so c=0, so v=32.2 t.
That the integral of velocity to get where how far the object as fallen since it was dropped. Let's call that distance d. d=16.1 t^2 + c. We know the object traveled 0 feet at time 0, so c=0. so d=16.1 t^2.
We're given the object fell 20 feet, so we just need to solve for t.
20=16.1 t^2
t^2 = 20/16.1
t = sqr(20/16.1) = 1.1146
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 14th, 2011 at 8:40:39 AM
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THIS TOPIC IS DISGUSTING. AND TO THINK THE WIZARD PARTICIPATED. YOU'VE LOST YOUR MORAL COMPASS.
July 14th, 2011 at 8:58:33 AM
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Quote: dihaigTHIS TOPIC IS DISGUSTING. AND TO THINK THE WIZARD PARTICIPATED. YOU'VE LOST YOUR MORAL COMPASS.
Take it easy. I see a math question and I answer it. Nobody would have taken an interest if the question was about dropping a rock from a 20-foot building.
By the way, the all caps is very obnoxious.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 14th, 2011 at 9:14:46 AM
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The Wiz was couth about it, notice how he used the word 'object' and not 'body'.
Oh, this thread reminds me of that Drowing Pool song; if you don't know it, Google it.
Oh, this thread reminds me of that Drowing Pool song; if you don't know it, Google it.
July 14th, 2011 at 11:37:06 AM
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Quote: dihaigYOU'VE LOST YOUR MORAL COMPASS.
Frankly, I think we make trade offs in cost of design and human safety all the time. Take the simple matter of home stairs. Many people feel that if we increased the height to length requirement by 50% it would save tens of thousands of people over decades. Deaths due to falls on stairs are roughly 1300 per year, and an unknown number of crippling injuries. However the cost of changing all the specifications is extremely high. Mostly because all the present available architectural designs would now be obsolete.
It's not that uncommon to see a waist high rail separating us from a 20 foot drop. To modify all public places for chest high rails would involve a big change.
July 14th, 2011 at 12:28:12 PM
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Paco -
The height / safety factor was discussed, in depth, in the
https://wizardofvegas.com/forum/off-topic/off-topic/5888-bad-day-in-texas thread.
I have a rebuttal for your comment, but I'll post it there.
The height / safety factor was discussed, in depth, in the
https://wizardofvegas.com/forum/off-topic/off-topic/5888-bad-day-in-texas thread.
I have a rebuttal for your comment, but I'll post it there.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
July 14th, 2011 at 10:09:59 PM
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Quote: DJTeddyBearPaco - The height / safety factor was discussed, in depth, in the thread. I have a rebuttal for your comment, but I'll post it there.
OK, I didn't read the other thread.
A mathematical analysis of an accident does not mean that you have no feelings for the victim. Most people of engineering backgrounds look at accidents, and get involved in plans to fix the problem.
July 15th, 2011 at 2:42:34 AM
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Quote: WizardI agree, but I get the answer a different way.
First, let's use 32.2 feet per second per second as the rate of acceleration.
Take the integral of acceleration to get velocity: v=32.2 t+c. We know velocity must be 0 at time 0, so c=0, so v=32.2 t.
That the integral of velocity to get where how far the object as fallen since it was dropped. Let's call that distance d. d=16.1 t^2 + c. We know the object traveled 0 feet at time 0, so c=0. so d=16.1 t^2.
We're given the object fell 20 feet, so we just need to solve for t.
20=16.1 t^2
t^2 = 20/16.1
t = sqr(20/16.1) = 1.1146
Thanks for the confirmation that this is an exercise in calculus!
As for what is proper and improper about this thread, I am at fault. I can see now it was a 'little much' to be talking about making a wager. However, just to have brought up an incidental mathematical question, that I view as acceptable. I apologize for the crudeness of the other aspect.
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
July 15th, 2011 at 5:42:29 AM
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Quote: odiousgambit
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?
Yes. Consider where this formula comes from - it is a direct result of calculus.
If there was no acceleration, then distance traveled in time t with velocity v is vt.
Newton realized that one can consider an infinitesimal interval of time (dt) during which the change in velocity is also infinitesimal, and therefore the distance traveled in that time is v(dt). The value for v is a*t (a is the acceleration - g in the case at hand), and therefore, the displacement with the infinitesimal interval dt at any given time t is vt(dt). Summing up all the small intervals from t=0 to t=T (the total time), one could get the entire distance traveled in time T. This summing up process is called integration, and is the fundamental part of calculus. Integrating vt(dt) yields vT^2/2 - the formula you started with.
(Sorry, I did not see Wizard's answer when I wrote this. He is essentially saying the same thing, the keyword being "integral"...)
"When two people always agree one of them is unnecessary"
