Here is a quick Apolo Ohno quiz. Which one of these pictures is fake?
If you picked picture B – you are probably correct. That is a picture of “Apolo” being catapulted into a pool of slime at the Nickelodeon awards show (click on the link to see the video – I don’t think I can embed it). Ok – time to crank out an analysis.
I think I could approach this analysis from a couple of directions. Since all I have is a crappy version of the video, I could just look at “could this be possible”? The other analysis I could do would be to measure his acceleration in free fall. Let me start with the second method.
Acceleration of Apolo
Using Tracker Video Analysis, I can look at the motion of Apolo as he is landing in the slime. Really, it is not a good video. The camera pans and zooms at the same time. Also, there isn’t really anything great to scale the video with and there could be some parallax errors. So, with that I get the following for the y-motion (unscaled video).
So, it should be constant acceleration. Is it? Too difficult to tell with only 5 data points. Here is the horizontal motion:
The horizontal velocity should be constant – this looks constant enough. So, from this I can’t really say for sure it is fake.
Suppose I assume air resistance is negligible – which really isn’t a terrible assumption in this case. Then if I know how far he is going to be shot, I can determine how long this should take. I can also see how long it took in the video. First, a couple of quick points about projectile motion (more info can be found here)
- For constant acceleration, the y-motion is independent of the horizontal velocity. This means that the maximum height and time of flight do not depend on how far the guy or ball goes.
- In the vertical direction, the initial speed when the ball leaves the throwing device (in the y-direction) is the opposite of the y-velocity when it returns to the same height.
- When you throw a ball straight up (or at any angle really), the time it takes to get to the highest point is the same time it takes to come down from the highest point.
Since I don’t actually know how far he went (I could estimate it) and since there can be two times for the same distance, I am just going to look at the vertical motion. From the video, Apolo is in the air for 3.6 seconds. This would give a time of 1.8 seconds to go up – how high would this be? Let me start with the kinematic equation:
You see the problem here – I don’t know the initial velocity. Ah HA! But I do know another trick. What if I look at the motion of going from the highest point back down to the initial level? Then the initial y-velocity IS zero. And this is the same height as going up. This gives:
This gives a height of about 16 meters or 52 feet. High school goal posts are 10 feet tall at the cross bar. Using tracker video analysis, this puts the top of the post at about 28 feet. The video isn’t quite clear (because of the creative editing), but it doesn’t look like Apolo goes over 50 feet above the ground.
I have caught you Nickolodeon. You can fool some people by having incredibly terrible video frame rate, but you can’t fool physics.
Oh, I know you are worried about landing in that small pool of slime – I agree that could be a problem. But don’t forget Professor Splash jumped from 35 feet into 1 foot of water. The slime was deeper than 1 foot – but if he came down from 52 feet WITH some horizontal velocity, that would be a problem.