# Dive into anything

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[Request] How many Gs will they experience when they land?

It really depends on how far Timmy was falling, because the speed that he was travelling before the sudden stop is vital. If he had reached terminal velocity, which is approximately 50m/s (rounded for simplification), and takes 1/10th of a second to reach zero after landing in the hero’s arms, that would equate to 500m/s2, or at least 50g.

This would require a fall from roughly 100 floors, though

PS: the g-force Timmy would experience, though still more than enough to kill him instantly, is actually vastly different from the amount he would experience if he had hit the pavement, unless the hero’s body doesn’t sag at all from the impact. If the hero does sag just a little bit, the g-force is decreased dramatically. If he hits the pavement, he stops instantly, and at this speed, the difference is exponential.

If he takes 1/11th of a second to decelerate Which is only 10% less time, he would be experiencing approximately 56g, which is 11% more force. If he had hit the pavement, and taken 1/1000th of a second (because we have to add a number for the calculation – and it technically would NOT really be an instant stop), he would be experiencing over 5000g of force.

So, technically speaking, “roughly the same g-force” actually means “still more than enough to die”

Okay but what if the person catching him was upside down and would soften the fall with their body by allowing timmy to fall on top of them? Would it still be lethal?

Additionally, there is the horizontal g-force of the hero slamming into Timmy.

The hero looks to be a little further than Timmy is high when the hero is running. If Timmy is already at Terminal velocity, then the total g-force of upwards acceleration and sideways acceleration would be double one alone.

If the comic showed the hero sliding under Timmy to reduce horizontal velocity, then we can pretend he cancels enough out. But instead, we see him leaping (adding more velocity) to Timmy.

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There aren’t very good specifics here, but we can see that Timmy fell at least 4 stories, which is about 50 feet. Above 30 feet is considered the “dead zone” where falls statistically become far more fatal. Plugging it into the Splat Calculator online, Timmy is going 40Mph (18 m/s) when he hits the deck. He dead.

Vsauce music

Or is he?

This comic shows that Timmy is caught in mid-air by a leaping man. This means that he transfers some of his momentum to the catcher. Imagine a friend running and jumping into your arms; you would stumble backwards, but they would also suddenly be going a lot slower. This is because they transfered some of their momentum to you.

We can compute this change in speed with conservation of kinetic energy by assuming Timmy, presumably a young boy, weighs 110lb (M_tim = 50kg) and the catcher, presumably older, weighs 165lb (M_catch = 75kg). I’m also going to give the benefit of the physics to our falling compatriot, and say that Timmy transfers 30% of his KE to the catcher, who catches Timmy at the peak of his jump, when he has 0 KE (he has some forward momentum, but we are only concerned with vertical velocity). I chose 30% because the catcher’s body is flexible and he catches Timmy pretty close to the ground, so he would not have time to absorb a lot of his Target’s energy. The maximum he could absorb without pushing off of Timmy would occur when they are going the same speed

KE=0.5MV² -> KE_timmy_falling = 8.1 kJ

After the catch, that KE is split, 30% to the catcher, 70% staying with Timmy:

KE_catcher = 2.43 kJ

KE_timmy_caught = 5.67 kJ

Reversing the equation for KE, we find everyone’s new speeds

V_catcher = 8.05 m/s

V_timmy_caught = 15.06 m/s

So Timmy is now going 33.6 mph. That’s still fast enough to kill (imagine going as fast as you’ve ever gone on a bike directly into a wall, or a car hitting you at medium speed), but with a human body to cushion the landing, he might just survive.

I re-ran the numbers, and it seems like, even if the catcher catches 50% of Timmy’s momentum, the kid still hits at 28.5 mph (12.73 m/s), so it doesn’t soften the landing much.

Moral of the story; leap-catching does help, but only if you can really pull your weight into things.

I’m going to assume our person had 1m, to decelerate and could cope with 10G of acceleration

so if we have out classic distance equation:

s = ViT + ((at^2)/2)

and work it backwards, we know the distance, acceleration I’m going to ignore the Vi term as we want the initial, or in this case end velocity to be zero.

t=((2s/a)^(0.5))=(1/100)^(0.5)=100ms

i.e. about they’d be doing about 10mps i.e. 25 mph, or the same as falling under gravity for 1 second. Humm, others have calculated about twice that speed…

Well F1 cars regularly have accidents where the car hits the wall at up to 200mph and in the depth of the nose-cone + crash barrier come to a complete stop. The drivers then hop out and are fine. Strapped in with a neck harness they survive this (>36g) with nothing more than wounded pride, so lets assume Timmy could survive 20g. Let’s also assume our hero jumped up to catch him so Timmy had 2m to decelerate:

28mps, which at 1G acceleration gives him :

(at^2)/2=(10*2.8^2)/2=39.2

So I think Timmy would be fine if our her could do that jump and decelerate him continuously.

Fletcher et al. estimated that an olympic clean and jerk weight lifter can exert 2000 watts during the clean portion of the lift, where the bar is brought from the floor to the lifter’s shoulders, over a period of 1 second, which is about 2,000 joules.

NASA has studied sudden forces, and apparently one is fairly sure to survive a flat impact onto a hard surface from up to 7m high. On an article about a girl who fell 25 feet off a roller coaster in 2017, a trauma surgeon reports that falls of 10m are survivable with serious injuries.

Timmy, appears to be falling from 6 stories, or roughly 60 meters (it looks like the building is appreciably taller than the other building, but not double, and therefore more than 4 stories). We’ll estimate he weighs 50 kg.

So, 50kg Timmy should survive a fall that imparts 5,000 joules of energy.

Our hero might be able to absorb 2,000 joules of energy, allowing up to 7,000 joules.

Timmy’s 6 story fall imparts 30,000 joules of energy.