You’ll survive the fall… and then drown in marshmallow fluff.
That’s a weird homework assignment. Are you studying pathology?
This, and other posts suggesting it’s not terribly lethal, are missing the head first part of the question, and probably also the concrete part.
I’m a teacher at an experiential education magnet school. In general I think kids do their best learning through hands-on activities. I don’t recommend that here.
Here is a study of falls vs mortality, it seems like the estimated height of 50% mortality is 10.5 meters, they don’t mention the surface the person lands on, nor what part lands first: https://www.ncbi.nlm.nih.gov/pubmed/22860503
Since the person is landing on concrete, and over the 50% mortality, I think it’s safe to say that chances of death are higher then 50% for a person falling from 11m, but not 100%, even head first, though it doesn’t look good, does not guarantee 100% as there are always freak factors.
Here is some interesting information that, while not about falling, is about speed vs fatalities (car vs pedestrian), it shows that chance of fatalities shoots up at speeds greater then about 40-45mph: Is 30 km/h a ‘safe’ speed? Injury severity of pedestrians struck by a vehicle and the relation to travel speed and age - ScienceDirect
Additionally, just to add, it make be of the person was drinking they would have a better chance of survival, that was shown in car accidents.
Just to nitpick it also does not say what planet, or moon one is on, where gravity may be different, though head first does indicate without a spacesuit, and infers some breathable atmosphere with a concrete surface of some type. But for a sci-fi story it is very possible to survive in certain locations.
A bike-helmet study published in the Journal of Neurosurgery: Pediatrics, wrote that 235 kg (520 pounds) or 2,300 newtons of force would be needed to crush a human skull. An average adult human is 62 kg weight and according to the free fall calculator in 11 meters you’d be traveling at 14.688 m/s plugging into F=MA we see that 14.688 * 62 = 910.656 Newtons. which would not seem to be anywhere near the required amount to crush a human skill. Now you could die from some other cause but I’d say that a guaranteed death is not, shall we say, guaranteed.
That seems surprisingly slow. Are you sure that’s right?
As I recall, the velocity after falling distance d = sqrt (2 x 32ft s^-2 x d)
which in this case would be sqrt (2 x 32 ft s^-2 x 36 ft) = sqrt (2304 ft^2 s^-2)
= 48 ft s^-1
Which is about 32.7mph.
That fits with the stats that show traffic collisions with pedestrians of the order of 20mph are considered survivable more often than not, whereas the fatality rate rapidly increases at speeds above 30mph. Not that falling head-first onto concrete at 32mph is necessarily comparable to being hit by a car at that speed - I’d rather take my chances with a well-designed car, to be honest.
Edit: I see drewder also corrected the speed above.
Is this a morbid version of those Scientific Wild Ass Guess questions from science competitions? The ones where the answer doesn’t really matter, but what matters are the process for determining the answer and the ability to show knowledge of scientific formulae and the math skills to use those formulae?
I think a good first step would be to determine the cross-sectional area of impact. Emma33559637, how long is your head from front to back, and how wide is it? Do you know the formula for calculating the area of an oval, or would you like assistance? For purposes of estimation, is it okay to presume that your head is flat?
You’ve got the correct speed, 14.688 m/s (32.83 MPH), but velocity has no place in the f = m*a equation.
f = m*a is challenging to apply to a collision (e.g. a collision between a skull and the ground). A different way to do it is to consider the kinetic energy of the skull at impact, and the distance over which it decelerates. This of course requires you to know the distance the skull moves during the impact event, and that depends on the compliances of the skull, the ground, and everything between them (skin, muscle, clothing, etc.). Helmets work because in addition to distributing the force of the impact over a larger area of the skull, the helmet compresses to allow the skull to be decelerated over a much greater distance.
Suppose you have a human head that weighs 5 kilograms. Drop that head from 11 meters, producing a velocity at impact of 14.7 m/s. Assume no helmet, and the head hits concrete, with the skull protected by only 5 mm of skin and muscle. For simplicity, assume constant force for the duration of the impact event. Calculate the kinetic energy of the head at initial contact, and assume that this kinetic energy is dissipated over a distance of one centimeter. What is the average impact force?
Now assume that in addition to 5 mm of skin and muscle, the skull is protected by a 4-cm-thick styrofoam helmet. What is the average impact force in this situation?
There’s a nice trick that simplifies this analysis. Instead of going through the machinations to calculate kinetic energy and then impact force, you can compute the ratio of the accelerating distance (11 meters) and the stopping distance (5mm in the first case). If you accelerate at 1G over 11 meters, then stopping from that velocity in 5mm will result in (11/0.005=) 2200G. Now you can use f=ma: a 5-kg head decelerated at 2200G will produce 108,000 Newtons of force. The force would never get this high because the unhelmeted skull will shatter into pieces. You better bring a mop.
The above scenarios assume the very simple situation of whether the skull gets fractured by the impact, without consideration of anything else. People do survive skull fractures, and people also can be killed without having their skull fractured. closed-head injuries can be fatal, and a high fall can be fatal without a head injury (e.g. cervical fracture/dislocation, massive blunt trauma).
“Recommended, eh?”
I used eyeballs, based on 11meters being 32 feet and 9.8 meters also being close to 32; so a 1 second fall.
I let errors propagate rather than finding a calculator. I figure at any speed over a mile in less than 3 minutes, collision is going to hurt a lot.
You can if you want to. The rule has been relaxed.
Maybe acrobatics.
Chance of survival would actually be a lot greater if the skull fractures than if it doesn’t. Though still really low.
Emma33559637, for a simple answer, yes, you can die from a 36-foot drop. At that distance, you have a little more than a 50% chance of dying. It’s more likely if the injuries are to your head or chest rather than other parts of your body.
From the OP -
Bolding mine, not a very interesting homework assignment. Yes you will die. Batman is fantasy.
I remember seeing these high dives back on 70’s sports shows like ABC’s Wild World of Sports or similar:
Rick Charls World Record High Dive 172’
I grew up near the Chesapeake Bay Bridge which has a vertical clearance of 187 feet (the deck would be several feet higher) for comparison and many people have committed suicide by jumping off the bridge over the years.
From a height of 172 feet, an online app gives me a speed of 72 mph on impact more than 3 seconds later. And the guy in the video does a flip and twist on the way down. :eek:
That dive. Holy Christ.
Now I have Holy Diver in my head. Which is a song i actually like.
Not for all the money in the world
It’s a heated pool, at least as long as the pumps last. Plus I’m in SoCal. Winter just means I wear shorts less often.