# A problem regarding a fiction

Recently I watched a fictional(I guess) video: a man is crossing the road while a truck accelerates towards him and a superhero flashes and saves his life by taking him out of the road. He was very fast, therefore only a flash could be seen. It seems like a silly incident though. After some time the question that occurred in my mind was 'if this happened in reality, could that man survive?'

This is my reasoning:

If the man had to collide with the truck it would create serious damages and this has been explained scientifically in many topics such as energy transferred to the body, force emitted, and so on. Also, I found that the acceleration of the vehicle performs a lower impact on the pedestrian. Nevertheless, everyone knows that more harm is done by a vehicle that goes with $$60 \;\text{km/h}$$ than $$5 \;\text{km/h}$$ at a collision. But in this scenario, the speed of the hero is exaggeratedly high(Find the video below). The speed of the truck is negligible in comparison. Thus the impulse on the man is massive when the hero catches him. Can a person endure such a great impulse? I heard that such a great change in momentum will disturb fluids in the person's body and feels extremely uncomfortable. And also can a person tolerate that acceleration? Thus the ridiculous thought that came to my mind was that the damage will be minor when the person had to be hit by the vehicle than is carried by the hero.

This seems to be a silly problem, but I am asking whether this could happen in the real world.

EDIT: Look for video here:- https://youtu.be/KJqhR2YSUXw And there is another similar video found on youtube:-https://youtu.be/EMOwFEB6Kz8

• It's the Superman catching problem. Jul 8 at 13:49

For an object to appear "flashed", I am guessing it would move at the same speed as say an airplane propeller, since they also appear "flashed". Such propellers have on average a rotational speed of $$\approx 2500rpm \approx 43rps$$ and the length of their blades are on average $$1.5m$$. This would give each blade (at the tip of it) a speed given by $$v=r\omega=1.5\times2\pi\times 43$$ and so $$v\approx 405 ms^{-1}$$.

When the hero swoops in and catches the man, and assuming they continue with the same speed, the change in speed felt by the man will also be $$\Delta v = 405ms^{-1}$$ and this ignores the impact damage the hero does by his mass. That is, we only consider the change in speed.

Let us be conservative$$^1$$ and say this happens over half a second, and so the acceleration felt by the man will be $$810ms^{-2} \approx 81g$$.

Now according to America's National Highway Safety Traffic Administration it is stated that

"The NHTSA standard for a sudden impact acceleration on a human that would cause severe injury or death is 75 g's for a "50th percentile male", 65 g's for a "50th percentile female", and 50 g's for a "50th percentile child". These figures assume the human is taking the impact on the chest/stomach, the back, sides or the head. The average value is about 65 g's."

As you can see, the man would have most likely been killed!

$$^1$$ Having seen the video closely, the whole process takes less than $$\approx 0.2 s$$, giving us an acceleration upwards of $$2,000ms^{-2}\approx 200$$g's. Such a scenario, where the person lives, is therefore extremely unlikely.

• Yes, but he'd be saved from being hit by the truck!
– jim
Jul 8 at 9:33
• I think I’ll take my chances with the truck! :) Jul 8 at 9:36
• Actually, if I may aggravate the case of the hero with some more rough estimates, we can consider that the person is acquiring the full speed of the hero once he has been displaced over a distance equal to his width. Let's say he's a thick guy, with width $L \simeq 0.5m$. At your chosen speed, this happens over $\frac{L}{v} \simeq 0.0012s$, yielding an acceleration of $a \simeq 34000g$, making an absolute mess all over the road. Jul 8 at 10:34
• Thank you @josephh .I found a link for the video. You may like to watch it.
– ACB
Jul 8 at 10:40
• Thanks. Though I am pretty sure that the video was made using Adobe After Effects or some similar program. But good to watch. Cheers. Jul 8 at 21:46