Can Wearing a Kevlar Helmet Protect You from Falling Bullets?

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Firing bullets into the air can pose a danger as they fall back down, potentially causing injury or death. The muzzle velocity of an AK-47 is approximately 710 m/s, while a modern Kevlar helmet can withstand impacts up to 610 m/s. Given air resistance, the bullet's return speed is significantly reduced, making it likely that a Kevlar helmet would provide adequate protection. However, if the bullet maintains its trajectory, it could still be lethal. The discussion references a MythBusters episode that explored this phenomenon.
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Homework Statement



Part 1:
We have all seen news footage from the Middle East in particular, where heavily armed gunmen toting AK-47 assault rifles fire their weapons into the air. What happens to the bullet after the trigger is squeezed? Can it be dangerous for people nearby when the bullet comes back down?

Part 2:
Assume the bullet is gyroscopically stable. Would wearing a modern army Kevlar helmet protect you?


I have found out that the muzzle velocity on an AK-47 is around 710m/s and a Modern Kevlar Helmet can handle up to 610m/s.
 
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1337 said:

Homework Statement



Part 1:
We have all seen news footage from the Middle East in particular, where heavily armed gunmen toting AK-47 assault rifles fire their weapons into the air. What happens to the bullet after the trigger is squeezed?
Unless it hits a duck, what goes up, must come down, somewhere.
Can it be dangerous for people nearby when the bullet comes back down?
Yes, it could be. In a rare case, it could cause death. The terminal velocity of a bullet can, unlike the low terminal velocity of a falling coin, be surprisingly rather high.

Part 2:
Assume the bullet is gyroscopically stable. Would wearing a modern army Kevlar helmet protect you?
Yes. Just don't look up.


I have found out that the muzzle velocity on an AK-47 is around 710m/s and a Modern Kevlar Helmet can handle up to 610m/s.
Due to air resistance, the speed of the bullet upon return must be less than 710m/s, a lot less. That helmet should, I would think, easily handle it, if your data is correct.
 
If the bullet keeps its trajectory it could be just as lethal. If it does not, then it will be limited to its terminal velocity and probably not lethal.

CS
 
Funny to suggest this here, but...

Check out Myth Busters. They had a show on this very myth.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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