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Comment by aatish | Hacker News Reader

Hi- I'm the author of the piece (on twitter at @aatishb) and am happy to field questions on the post. Do people accept that the video isn't faked? The data isn't perfect, but it was good enough to convince me that the video is real.

Here's a follow up question, that I haven't thought much about. Assume that Rugland launches the first ball at 64 degrees and at 14.4 m/s (about 32 mph). 1.5 seconds later, and 1.5 meters ahead, he kicks the second ball. (So far these are the numbers I get from the data). My question is, given the size of a football, how accurate does he need to be in the launch speed and angle of the second ball, in order to be able to strike the first ball?

You might need to assume a reasonable range for the launch speed to work this out.

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Here's a first-order approximation. I'll assume the angle is perfect and work out the speed range. The first ball decelerated to maybe 8 m/s given its altitude at collision and some loss to air friction. If the ball is 25 cm wide, it crosses its own diameter in 1/32 second.

Assume the distance of the collision is 10m from launch and occurs 1.7 seconds after the second kick. The margin of error on the arrival time is 1/32 / 1.7 = 1.84%. Using your launch speed centered around your value of 38 mph = 16.9875 m/s, that means the possible range was 16.675 to 17.300 m/s. Interestingly, that's a difference of 1.4 miles per hour, which is also roughly the precision of velocity that baseball pitchers can produce on demand.

By the way, there's more variables on the inputs to the second ball. The timing of the kick is important and controllable too, creating a three-dimensional map of inputs. This could be transformed into and visualized as a 3D graph, showing all the combinations of speed/angle/timing that will result in a collision.

Also, the left-to-right angle must be on target too or the balls won't be in the same vertical plane for any collision at all.

About the vertical angle that you assumed to be perfect: I don't think that is critical. If you hit the second ball a bit higher/lower than intended, it crosses the trajectory of the first ball higher/lower than intended, so it must be at the intersection point earlier/later. Luckily, you get some of that for free, as the intersection point will be closer by/farther away.

All else being equal, the harder you can kick, the easier this gets. The lower the arc of the first ball, the smaller the angle of intersection between the two trajectories, and the easier the hit. You can get a lower arc by giving the ball more horizontal speed, keeping vertical speed the same (just decreasing vertical speed won't help; the first ball would hit the floor before you can hit it with the second ball)

Of course, all else isnt equal; directional errors likely are some function increasing with both distance and ball speed.

I think your assumption that good physics == not fake does not hold for certain classes of faking, i.e. simulating the collision first and modifying the ball positions (or creating one or both balls wholesale) to match.

I mention this not to cast any doubt on the kicking video, but because there are a lot of good simulation tools nowadays and faking something up by working out the physics first is only going to get easier.

Well, if fakers make the effort to do the math (and physics), more power to them. It just makes this kind of video forensics a more interesting challenge. :)

Here's another example of a physics based take-down (by Rhett Allain) of that eagle lifting a baby video that was doing the rounds. http://www.wired.com/wiredscience/2012/12/eagle-picks-up-a-k...

Analyze this - https://www.youtube.com/watch?v=ZQX8FakToj0 :)

Nice work, but these types of videos always annoy me. Anyone with the basics of athletic skill can perform these stunts with enough tries -- which the guy admitted to taking several tries. Some of the pure-power moves are out of the question for a lot of people, and those are definitely cool, but kicking balls into trashcans and basketball hoops is not.

The exception would be doing several difficult moves in a row without fail.

Yes, I could get a video of me doing a lot of these stunts. Great. Could I get all of them to happen in an afternoon of trying? Probably not. It would take a long time and a lot of luck to get any one of them.

An interesting, and far more skill showing (imo) version of this video would be to show how close they were on each of the tries - If for example he was within a couple of meters of collision each attempt, I would call that very high skill. But if the other attempts were dozens of meters apart, the skill would be much lower.

There are a handful of uncut scenes in the video where he repeatedly hits his target.

That is an awesome analysis of video and working through the physics.

Complete aside: Mind exploded from unit mismatch. Miles per hour then meters? Gah....

Just please dont use gradians for angle measurement :)

haha - the 32mph was originally 14.4 m/s. Given that the top story here today is a white house petition to adopt the metric system in the US, I should know my audience better :)

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