Could This Pneumatic Lab Prank Work?

I hate April Fools day. It used to be cool, but then it became this day of internet anarchy. Really, the only thing I consistently enjoy is the ThinkGeek Catalog for April 1. In particular, I like the PLAYMOBIL(TM) Apple Store Playset.

Moving on. Here is a popular prank video for this year's Fool-festivities. (hat tip to Brian for the suggestion):

Now for the physics. I am not going to determine if it is fake or not. It's fake. So, what is next? The next thing is to see if you could really do this. What would I have to do to shoot something at a person and have them recoil like that?

Data from the video

What can I get from the video? Not much, just an estimate. What is the victim's recoil speed? Looking at it frame by frame, it looks like he goes back about 2 meters in 0.2 seconds. This would give a speed of:

How long did the collision between the foam projectiles (I guess that is what it is) and the person last? From my best estimate looking at the frames, I am going to go with around 0.07 seconds. Probably the only other thing I can estimate is the person's mass (say 65 kg).

Idealized version of the collision

Here comes the spherical cow part. Here is a diagram:

For this simpler version of a collision, I am assuming:

• A person mass m_p and a foam projectile mass of m_s.
• Before the collision, the person is at rest and the foam thingy has a speed of v_s
• Ok - here is the difficult part. There can be all sorts of collisions. Let me assume that in this case the foam projectile completely stops after the collision and the person recoils with a speed v_r.

For a collision, the momentum of the stuff before (in the horizontal direction - let me call it x) is equal to the momentum after the collision. In the x direction, this becomes:

Like I said before, I can guess the person's mass and recoil speed. I don't know the projectile mass nor do I know the speed it is shot at. I am going to have to make a wild guess at one of them. How about a foam projectile mass of 5 kg (yes, that seems quite large). If that was the case, how fast would it have to be shot?

290 mph foam launcher. It could be done, but it would be dangerous. If the mass of the foam was half as much, the launch speed would be even higher. Crazy high. Ok, remember I made some collision assumptions. Lots of other things could have happened, the foam projectile could have recoiled back or even gone in the same direction as the person.

Acceleration of the Person

One more thing. The acceleration of the person is a good way to estimate injury. In this case, the person went from 0 m/s to 10 m/s in about 0.07 seconds. This would be an acceleration of:

According to NASA's human tolerance of g-forces, this is in the acceptable range for such a short time period. That is good because if this is indeed fake, like the fakers have a cable attached to the person to pull in him back. So, he probably did really have that acceleration. The gun probably just shoots some really low mass foam peanuts or something.