#48: Smacking the Bullet
Brandon, Kurt’s co-worker asks
I was wondering something. If a bullet were to be fired at a persons head from, letâ€™s say, 40 meters away, is it possible to use your hand to alter the path of the bullet to miss your head? Pretend the person times it perfectly and strikes the bullet with their hand on the side of the bullet. Would this affect the path enough to miss, or what would happen? Thank you!
So, you want to smack a bullet away, like it’s a mosquito. Interesting theory. Let’s do the math.
For this answer, I’m indebted to a party who shall remain nameless, who bolstered my flagging math skills and pointed the way to the answer.
Let’s do the variables first.
v = the velocity of the bullet. For our purposes, we are ignoring wind resistance and the effects of gravity.
t = the time it takes for the bullet to travel to your head.
d = the distance between your hand and your head.
F = the force applied by your hand to the bullet when you whack it.
m = the mass of the bullet.
a = the acceleration imparted by your hand to the bullet when you smack it.
h = half the width of your face. This is the distance you need to move the bullet so it doesn’t hit you.
Now for the equations.
t = d / v
The time it takes to travel a certain distance is the distance divided by the velocity.
F = m * a
a = dv/dt
Acceleration is the deravative of velocity with regards to time.
F = m * dv/dt
The slap will not affect the forward velocity; we are assuming
the strike is perfectly sideways.
F= m * dvy/dt j
Since the forward velocity only affects how hard the bullet has to be
hit, this can be rewritten as
F/m dt = dvy
We are assuming that the force applied is constant for a time duration, so we integrate.
The above equation, when integrated, yields:
F * t / m = vy
How to play with this vy piece?
This one requires a little more calculus than the last:
vy = dy/dt
h = (F*t^2)/(2*m)
Assembling and rearranging:
F = (2*h*m*vx^2) / (d^2)
Okay, we have a workable equation. Let’s fill in some estimated values.
h = 0.1m
d = 1m
m = 0.01kg
v = 1000m/s
F = 20,000 Newtons!
That’s a lot of force. It equates to approximately 4,000 pounds of force.
However, the average person’s fist, when swinging, delivers about 2,000 Newtons to their target. That’s 400 pounds of force.
So, in order to save your pretty face, you’d need to deliver a smack to the bullet that is 10 times more powerful than average, and that’s assuming you hit it directly on the side, and that your hand is impenetrable. Probably unlikely. What would really happen is that your hand would be damaged as well as your head. Not a pretty picture.
This is also not a pretty picture. Think about it.