It’s been a few decades since my college physics class. I can’t remember exactly how to setup the force vectors.
Hero catches a child in this video. He obviously absorbs an impact, but stays on his feet. It certainly helped that the child didn’t strike his torso.
How how much force does he absorb?
It’s a 2 year old child. Can we assume a twenty pound child and a two story window? How about three stories?
W=F*s.
If the child is accelerated by a force m*g over a distance of, say, 6 m; and if you decelerate it from top speed to zero over a distance of 1 m (perfectly possible, if you can catch it at breast level and remember to flex your knees) then the average force you have to put up is six times the child´s weight (say 120 pounds).
Quite a bit, but doable for a fit person.
We can’t really assume either two or three stories because “story” is ambiguous. In much of Europe, the first story is the first elevated floor, but Americans would call that the second story. The story seems to come from both Reuter’s (nominally American) and AFP (French).
So 10-20 meters seems like the right range
A 10-kilo child falling from, say, 9.81 meters above the catcher would accumulate about 481 Joules when she made contact with the catcher.
That’s about as much kinetic energy as a 9mm bullet develops upon leaving the muzzle of a pistol. But comparisons like that don’t mean much.
If the toddler fell about ten meters and her rescuer slowed her to a stop in 0.1 seconds, that would work out to a 10g average deceleration, requiring about 981 Newtons, or 220 lbs of force.
Double the drop height and you’ve quadrupled the toddler’s energy, a phenomenon that would otherwise require amphetamines. 
That’s about half I calculate - mgh=1000 J
That seems about right based on what I saw in the video. He absorbs a lot of energy breaking that toddlers fall. The adrenaline kicked in and he didn’t noticably seem effected.
I bet he felt it in his back & shoulders the next day.
Thank you for your help.
It looks like the child’s feet still hit the ground. I’m sure our hero slowed down her fall, but he did not absorb all the kinetic energy.
Nitpick - (This is the Dope after all)
In Europe, the first storey (note the British English spelling) is the same as the American first floor. However, the European first floor is the same as the American second floor. The American first floor is the same as the European ground floor.
A single stor(e)y building is the same in both continents.
Looks to me like the important part is the girl landed on her feet. He kept her upright as she slid through his grasp. Her head or torso didn’t have to absorb any of the impact.
Good catch—pun intended. I was being too clever by half, as it were.
The instantaneous velocity after ten meters would be about 14 m/s:
V[sub]i[/sub]=sqrt(29.8110)=14
E[sub]k[/sub] = 0.5mv[sup]2[/sup]
= 0.51014[sup]2[/sup]
= 981 J
Cheers!
The stor(e)y/floor dichotomy is an English-language one. You seem to be conflating Britain with Europe. Many Brits and Europeans would take issue with that. Many wouldn’t. It’s ambiguous, non?
The premier étage is the second floor in French. Rez de chaussée means “street level” in English, so story/floor doesn’t really seem relevant in French[sup]1[/sup]. I can’t really speak to other European languages/countries. Hopefully, others can.
My point was only that there was ambiguity in the linked story regarding how far this poor girl fell. Are you seriously arguing otherwise?
[sup]1[/sup] The English “story” (like a tale of the Canterbury variety) is histoire in French, and I’m pretty certain that using it to refer to a building would make zero sense in French. The root is from the Latin historia, but even the OED acknowledges that “story” in the architectural sense may or may not share that root. It’s—wait for it—ambiguous!
True - I did conflate Europe with Britain. My bad.
And I am not arguing at all about the ambiguity in the linked story - I totally agree with you on that.
So would the child.
All that force had to pass through her back & legs at the points where his arms caught her. Would have been some impressive bruises on those parts of her body!
P.S. In this case, he didn’t catch her back & legs in his outstretched arms, like in movies. But probably a more realistic & effective way than in the movies.
Being caught “movie style” would be a good way to get whiplash, I expect. Suddenly stopping the torso from moving horizontally without the head being braced on something is how that happens.