Dot Physics

Giant water slide jump

Thanks to Nick for showing me this video (Check out his blog – Fine Structure):

Wow. That was my first reaction. My second reaction was: no way. Is this real life? I just don’t know. How hard would it be to find out exactly where to place that pool and where did they get the water from? Obviously, this one requires some analysis. First, on the VAS for this video: 4/8. Not too good. Oh here are the questions I would like to answer:

  • What is the guy’s acceleration after he leaves the ramp?
  • What was his initial velocity leaving the ramp?
  • How high above this would he have to start?

Ok. Time for Tracker Video Analysis. Here is the y-motion for the ‘flight’:

i-785c0aebb08e5dcc59924052f3554d1f-data_tool_5.jpg

Notes:

  • The unit of scale is the height of the ramp.
  • There is an obvious perspective problem. As the camera pans, the angle between the motion and the camera is not constant and not perpendicular. I have no simple way to correct for this (yet).
  • From this, the acceleration is about 4 ramps/s2.
  • At this point, I can’t really tell if it is fake or not. The motion does not fit a parabola very well, but that could be because of perspective issues.

Now, if I assume that the acceleration in real life is 9.8 m/s2, then the ramp would be 2.45 meters tall. Using this new scale, I can look at the horizontal motion:

i-12fe0c7fa56b44f10721f190f7780769-data_tool_6.jpg

This looks linear-ish. From this, the horizontal velocity is mostly constant at a value of around 16 m/s (which is about 36 mph for the metric-challenged). At least I have enough info to make some calculations. Note that 16 m/s is the guy’s horizontal velocity, not the total initial velocity. The initial vertical speed can be determined by looking at the time in the air. (here is a review of projectile motion) If I assume that the guy starts and lands at the same height, then I can use:

i-b08772c7e0ca503fcf4cbe53121fbb0f-la_te_xi_t_1_58.jpg

Since y and y0 are the same, I can solve for the initial velocity:

i-94b70ef19347ef8741246c88229e98a1-la_te_xi_t_1_59.jpg

From the video, ?t = 2.1 seconds. This gives an initial y-velocity of 10.3 m/s. This will give a total initial speed of:

i-89801dfc0c4ef63cb7d89e33fb9c63ab-la_te_xi_t_1_60.jpg

Putting in the values for the x- and y-velocity, this gives a magnitude of the initial velocity of 19 m/s. Why do I care about this velocity? Two reasons. First, I can estimate how high up the hill the guy would need to start to get this speed. Second, this is the same speed the guy will hit the pool. So, I can estimate the acceleration when he lands and see how deadly it would be (I already suspect he should be ok – think about professor splash)

How high up the hill would he have to start? If I ignore friction (always a good place to start), then I can use the work-energy principle to calculate this. Let me make a sketch.

i-0bf9386f1887431bef30f7dc456ee098-untitled_29.jpg

The work-energy principle is great to use here because it essentially deals with change in position. I will start with the Earth-guy as my system (this means that there will be a gravitational potential energy and NOT work done by the gravitational force). When working with the work-energy principle, you need two positions. In this case, that will be at the top of the hill and at the top of the ramp. During this motion, there are only two forces acting on the guy: the normal force from the ground and the gravitational force. The normal force does no work since it is always perpendicular to the direction the guy is moving. Gravity doesn’t do any work because I am using the gravitational potential energy. If the guy starts from rest at the top of the hill, and I set the zero gravitational potential at the top of the ramp, then:

i-26b48f1e2aeb1eb175fd1b6c24b197e1-la_te_xi_t_1_61.jpg

I didn’t want to be too confusing about the velocity in the above expressions. That is the velocity at the top of the ramp. If I wanted to be consistent with the stuff from before, this would be v0. Using this stuff and solving the for the height above the ramp, I get:

i-9c05069a187b0f313509a18d06de05e4-la_te_xi_t_1_62.jpg

Notice that this solution does not depend on the mass of the guy nor does it depend on the angle the hill is inclined. If I plug in the value for the speed at the top of the ramp, then the starting point must be at least 18 meters higher than the top of the ramp. If there is significant friction it would need to be even higher.

It is very difficult to estimate the height of the starting point because of the angle the camera is viewing from. There is one thing that does not change with perspective though – time. I can get the time it takes the guy to get from the top of the hill to the bottom of the hill and calculate how steep the hill would have to be (again assuming no friction). From the video, this is about 3 seconds. The ramp looks pretty big, but I am going to use the velocity at the top of the ramp as though it were the velocity at the bottom of the ramp just to get an estimate of the angle of the ramp. Ok, so if he goes from 0 to 19 m/s in 3 seconds, then his acceleration (average) would be:

i-4dfda08505280d048442e78d9bc7ef77-la_te_xi_t_1_63.jpg

So, if this were a hill at a constant slope with no friction, how steep would it be? Here is a free body diagram of an object sliding down a slope.

i-5170031b0083c06d701e3ffd3dfbedac-untitled_30.jpg

I want to find the acceleration down the plane as a function of the angle of the plane. In this case, the only force acting in the direction of acceleration would be a component of the gravitational force. This gives:

i-af741e6f71721430c2b63b937a63a5bb-la_te_xi_t_1_65.jpg

If I put in 6 m/s2 in for a, then I get an angle of 40 degrees. Pretty steep – but it is a mountain I guess. I guess this is real. But there are still some things to investigate. I will leave the following questions for homework:

  • Suppose you are planning this “stunt” and your initial velocity is off by dv (some small amount). What would the resulting change in range be? If dv = 0.5 m/s, would the guy still land in the pool?
  • Suppose the coefficient of kinetic friction was 0.1. What would be the new velocity at the top of the ramp? You can assume that the hill is straight.
  • Estimate the acceleration of the guy when he hits the water. Look up the NASA g-force tolerance tables and see if he is ok.
  • Where did they get all the water to fill up the pool?
  • Who inflated the pool and how long did it take if they just used their lungs?

Homework hint. If you look at that Professor Splash jumping into a foot of water, it will really help. In that analysis, Prof Splash is going about 15 m/s before hitting the water. Yes, that is slower than this guy, but this guy lands in much deeper water (maybe 3 feet?) and at a non-perpendicular angle (which means he has a greater distance to slow down).

Update:

As pointed out in the comments, this is indeed a fake video. I lost. Anyway, there are some points that are still true.

  1. This is not impossible. Even for a computer. We used to bullseye wamprats back home and they are not much bigger than 2 meters. No really, it could be done even if it would be stupid to do so.
  2. The pool should be plenty deep enough to land in. Look at professor Splash jumping into 1 foot of water.

Comments

  1. #1 Lori
    August 7, 2009

    This is a very interesting analysis! How do you extract the video to get it into an analyzable format?

  2. #2 Rhett
    August 7, 2009

    @Lori,

    I used NetVideoHunter plugin for FireFox to download the flash movie (.flv). I then use MPEG StreamClip to convert it to quicktime format. There are many other options for downloading videos, but I find this combo to be the best.

  3. #3 John
    August 7, 2009

    Everything looks convincing until the landing.

    He hits the water at that angle, and suddenly falls downwards into the pool…?!?

    He would most probably bounce straight back out off the water and bury himself in the hill behind, or less likely, empty the pool, split it open at the rear and end up in the ground.

    Whichever way you slice it, there’s a huge amount of lateral energy gone missing.

    The acting at the end isn’t very good either.

  4. #4 Lori
    August 8, 2009

    Rhett, Thanks for the info about NetVideoHunter, that worked great. I also downloaded the MPEG StreamClip application, but it will not open the .flv file. I did manage to convert it using Zamzar.com. I am trying to find the simplest way to accomplish this because I will be doing it with my high school physics students. Thanks for creating this blog, I plan to use it with my students!

  5. #5 Paul
    August 10, 2009

    If you use GraphClick or NIH ImageJ (free). You can get an estimate of the landing speed. Assume that the tucked ball is approximately 1m in diameter two frames before it lands you see movement of about 2-3 lengths in 1/25 of a second. This translates to a much higher speed than you report here. This doesn’t include any parallax error and the horizontal component is consistent with the estimated distance from the launch point to the landing (~120m).

    The net effect is that it is hard to believe a human can survive a landing moving that fast. (There are many other suspicious clues but this relates to the physics)

  6. #6 David
    August 10, 2009

    I’m not sure about this video. The analysis is most excellent, but I’m feeling similar to John (see above) as to authenticity. The pool itself barely flinches. Even my 8 year old daughter’s pool wobbles wildly when it’s just her splashing around; and this guy was FLYING!. Also, the ramp ride looked a tad too smooth given that he was traveling down a hillside. All those bumps would have been impossible to control for and would have sent him right or left several degrees. Great calculations on the X and Y axis stuff, but the Z axis seems way out of whack. I’m calling B.S.

  7. #7 Rhett
    August 10, 2009

    @David and @John,

    I agree that the movie seems fake – that is what prompted me to analyze it. I am still open to the possibility that it is fake, but I don’t know how you would fake something like this.

  8. #8 Paul
    August 10, 2009

    I tried analyzing the whole video and found it difficult to account for the camera motion. All I could do was investigate a few frames here and there where the camera movement was slight relative to the flying object. The object is moving way too fast for the relatively gentle landing. There is a site where a someone investigated the video from the point of view of special effects:
    http://www.juicetheblog.com/2009/08/05/unbelievable-waterslide-compositing-walkthrough/
    I believe this video is a great goof. Still I want to use it in my class as a kind of demo, fully informing my students of its suspicious nature.

    Another thing to consider is that the edge of the launch platform is flat! If you were to even try to do something like this wouldn’t you build it with a fairly significant concavity so that I would be assured of being launched in a particular direction (decreased lateral uncertainty)? I would have found the video more believable if he had landed in a small pond rather than a kiddie pool.

  9. #9 Mike
    August 12, 2009

    Viral..I mean seriously. Why do people even try to legitimize?

  10. #10 Joseph Smidt
    August 22, 2009

    Dugg for awesome physics analysis.

  11. #11 Settlement
    September 2, 2009

    Apologize for my bad english, I deem its a winsome piece of your writing. Well I have faced alot of difficulties in this form but your article discretion definately escape me in future. Thank You

  12. #12 Ben
    October 9, 2009

    Mike :

    Viral..I mean seriously. Why do people even try to legitimize?

    Exactly.

    As-if for one second its real !! WTF ?

  13. #13 ULTRA RAD
    November 16, 2009

    Ill lay it down like this. IF one of you can set this sh!t up I will give it a try!

  14. #14 Jim
    December 26, 2009

    I AM convinced that this is fake, let’s make that clear.
    The most compelling evidence to me is the overly gentle landing…..
    But… A couple of points:
    1.) This as an AWESOME fake.
    2.) Will people PLEASE stop asking the stupid question: how could they tell where to put the pool?
    Folks….send a sack of dookie down the ramp weighing the same as the dude, and put the pool wherever it lands.

  15. #15 kt
    December 28, 2009

    Hey ya’ll,
    If you have ever slid down a long hill in the winter, you watch this and wonder why the very obvious undulations in the hillside don’t bounce him in the air-even a little bit.
    He ought to be flying 2-3 feet in the air at least twice before takeoff.

    Btw. Ever skipped rocks off the water? There you go.

    It’s a great video, nonetheless.

  16. #16 Richard Lawrence
    February 5, 2010

    this is a very interesting analysis. I would like to do something like this slide jump for real, i would like to do the biggest slide jump ever done, idealy in a large city for maximum impact. do you think you could help me to figure out how big i could make the jump without killing myself? please e-mail me pilch2000@hotmail.com if this is something you would be interested in helping me with

  17. #17 Rhett Allain
    February 5, 2010

    @Richard,

    I am afraid to help you. What if something bad happened? No really – the problems that you will face will most likely be engineering related (which I am not an expert at).

  18. #18 Richard Lawrence
    February 6, 2010

    i appreciate what you are saying and agree the engineering will be an issue, i have a few ideas for this part and am in the early stages of finding a sponsor so it can be done properly and as safely as possible, however i would still need someone who could do the mathermatics of figuring out my speed, tragectory, hights and landing site etc, i have a few idea on how to make it safer and would appreciate the chance to disscuss these with you.

  19. #19 Rhett Allain
    February 6, 2010

    @Richard,

    Why don’t we start with this – was there some question you had about the post? I will be happy to elaborate on any aspect of that if you like.

  20. #20 V. infernalis
    May 20, 2010

    Note: This week’s Mythbusters tested (and busted) this myth. They had a 200-foot, 24 degree ramp with a 30 degree kicker at the end, and ended up with about a 70 foot distance at ~30 mph.