Blob jump? What is that? Check it out.

OK. I have looked at this before — but it was a long time ago. Perhaps it is time to revisit the blob jump. Why? Because the creators of this video essentially begged me to do in the way it was made.

• First, it is a cool video with a cool toy. Who doesn’t like to see people flailing and flying through the air?
• The video is perfect for video analysis. It has the camera far away, stationary, and perpendicular to the motion. It is also in HD. What more could I want?
• From a physics perspective, it is a fairly simple problem.
• Finally, the video creators listed some numbers for the height that I can check.

Let the analysis begin.

The Physics of the Blob Jump

How does this thing work? Who invented it? Where can I get one?

I guess the best explanation for how it works is that it is like a giant see-saw. When people jump down on one side of the huge airbag, the other side goes up. If you consider small energy losses, then the work done by the bag in slowing the falling people down is the same work done on the launched person.

If you want to find out how high a person would go, you could use the work-energy principle. If I consider both the people, the blob, and the Earth as the system — there is no external work. Using the jumping people starting on the platform as the starting position and the launched person at the highest point — I would have this for a diagram.

The nice thing about these two positions is that in both, the objects are at rest (well, if you ignore the horizontal motion of the launched guy). This makes the work energy principle look like this:

Actually, now I feel bad for leaving out the horizontal velocity. If the launched dude is still moving at the highest point, this would be the work-energy principle:

I hope it is clear that m₂ is the mass of the launched dude. Also, if you solved for h₂, it would tell you the maximum possible height. However, it would be less than this value since I am sure you would lose some energy in the blob collision.

Anyway, that is how the thing works. The greater the mass of the jumpers (m₁) compared to the mass of the launcher, the higher the launched dude will go. For the video above, they used three men for the jumpers. You can see the result.

Checking their values

I don’t know the masses of the jumpers — so it seems there isn’t much to do. Oh wait, I can check their numbers. They said the launched dude went 17 meters high — but did he? How could I check this? Video analysis with Tracker Video (oh, free and runs on Mac OS X, Windows, and Linux). That is how.

If you aren’t familiar with video analysis, the basic idea is that you can get position and time data from a moving object in each frame of a video. There are some tricks, but that is the basic idea.

In the video, there is a frame shown with the starting height of the jumpers. Here it is.

If this is the correct scale (9.9 m), then when I look at the vertical motion, it should have an acceleration of -9.8 m/s² like all free falling objects do. Here is a plot of the launched dude’s vertical position vs. time for the first shot from the side.

How do you find the acceleration from this quadratic fit of the data? Consider the following kinematic equation:

Comparing this to the fit equation, you can see that the “a” term is the same as the -(1/2)g in the kinematic equation. This would mean that the value for g in that video would have a value of 2.25 m/s². Something is wrong. Either their measurements were WAY off, or this shot is not in real time but rather slow motion. Drat. It must be in slow motion. I guess I should have realized the time scale was wrong. The launch dude was in the air for over 7 seconds.

So, how do I find the time scale? Well, there is another shot that seems to be in real time. However, this shot doesn’t show the whole flight of the launched person. Drat. OK, let me try looking at the three jumpers. You can see them just for a short while in the slow motion video. Also, there is another video showing them jumping that seems to be in real time from the view at the top of the jumping platform. If I assume this top of the platform view is in real time, then they fall for 1.32 seconds.

Let me use this free fall time to find both the height of the jumping platform and their speed at the bottom. Suppose they jump from a height h in a time t and starting from rest, this would be:

Using a time of 1.32 seconds, this gives a height of 8.53 meters. Oh dear. This is close to the stated 9.9 meters, but not quite. Oh wait. This says they FELL 8.53 meters. The video listed the height from the ground to the tower. So, maybe I am OK. Here is shot using Tracker Video’s measurement tools.

I know it is difficult to see. However, if I set the height of the platform at 9.9 meters, then it looks like the center of mass of the jumpers drops about 8.4 meters. Close enough to 8.5 m for me — especially considering that it is difficult to tell exactly where the center of mass starts.

What about the final velocity of the jumpers? Using the definition of acceleration:

Now, here is the vertical motion of the jumpers (just at the end of their fall) from the slow motion video:

If I once again assume time units of sec’, then the final velocity of the jumpers (with just 4 data points) would be -6.95 m/s’. If I assume this is also a speed (in real seconds) of 12.9 m/s, then I can find the relationship between s and s’.

Let me make a wild guess. Let me guess that the slow motion video is really in half speed. Here is the vertical data of the jumper assuming the video is half speed.

This would still put the acceleration at just 8.97 m/s². So, you see I have some problems here. I can assume the stated distance is correct and then find the time step for the slow motion video. Or, I can assume the slow motion video time step is half speed and then find the distance.

Assuming the platform is 9.9 m

If indeed the jumping platform is 9.9 meters, as stated — then how high did the launched dude go? From my data, the launch guy started at -11.243 meters and reached a highest point of 4.003 meters (it doesn’t matter where the origin is — but in my case it is in the center of the video). This gives a change in height of 15.24 meters. The video claims 17 meters. OK, looking at their scale picture it seems I was measuring from where he left the blob and they were measuring from his starting position. If I go back and look at where he landed, then the maximum height above the water would be 16.68 meters.

I assume that the launched guy actually started somewhere above the water level. This means that his maximum height is probably slightly less than 16.8 meters — so not 17 meters. I could be wrong though. There could be some perspective errors (not sure how far away the camera was). However, this plot of the horizontal position of the launcher looks good (constant velocity).

I take that back. There does look like there is some perspective errors. Notice how the position deviates both at the beginning and end of the flight (by just a little). Perhaps the camera was too close to the scene. This would cause the beginning and end motions to be farther away (and thus have a different scale) than the middle of the flight.

With that, I think it is possible the launched guy made it 17 meters. It was close though.

Homework questions

I think this video can make an excellent lab or class activity. There is a ton of stuff left to look at. Here are some suggestions:

• What is the ratio of the masses of the jumpers to the launcher dude?
• How far horizontally did the launched dude go?
• If he had instead been launched straight up, how much higher would he go?
• What was the acceleration of the launched dude during the launch? Do you think it hurt?
• What would be the minimum depth that the water should be so that he can land without serious injury (some guesses needed here).
• Could you estimate the energy loss in the blob?