Dot Physics

Tail-Drop Analysis

I don’t know why they call it a tail drop. Here is a video:

The link I clicked that brought me to this video said the equivalent of “OMG!” That is not what I thought, really I am not sure what is so impressive (except that he didn’t fall off the skateboard). If the original poster was impressed with the height of the fall, he clearly has not seen the 35 foot jump into 1 foot of water by Professor Splash.

Anyway, it seems like a simple video to analyze with Tracker Video Analysis. Mostly because the camera is stationary, there is little perspective problems and the motion of the object is perpendicular to the camera. So, here I go. The only problem with this video is that I don’t actually know how to scale it. I picked the height the skater fell as my distance of 1 h. Then, getting vertical data for the fall and the landing, it would look like this:

i-931e0c3b2a91bc13a030b12d9e42a409-2010-05-26_data_tool.jpg

For the first part of the trick, the skater is falling with a constant acceleration of -9.8 m/s2. For constant acceleration, the jumper’s position should agree with:

i-3ac8e8d579efa15a3899cd8ad466bdc5-2010-05-27_la_te_xi_t_1_7.jpg

Here the initial y-velocity is zero (since he starts from rest). So, if I fit the equation for a parabola to the y-motion, I can get the acceleration. Here is that fit to the first part of the motion.

i-e1a2c323022d0fbc9a542ca5c2dda4ab-2010-05-27_data_tool_1.jpg

From this, I get an acceleration of -2.4 h/s2 (remember h is the height of the drop). If I then also assume this stunt is on Earth, then:

i-df3406af012a203dca701342aafdcd55-2010-05-27_la_te_xi_t_1_8.jpg

A drop of 4 meters seems reasonable. Now, I can get the acceleration during the landing by doing a similar thing (I am going to go ahead and re-scale the video so that it will be in units of meters instead of “h”). Here is the parabolic fit of the vertical position during the landing.

i-72a30b39d6e4c8333d19090b42af328c-2010-05-27_data_tool_2.jpg

The vertical acceleration during this part is about +9.8 m/s2. The skater makes this acceleration manageable by doing two things. First, he lands on a slope. This increases the time (and thus decreases the acceleration) that he is changing his speed. Just imagine if he landed on a flat surface – ouch. The other thing the skater does is to continue to move his center of mass downward during the landing. This also increase the time over which he slows down. Remember, acceleration in the y-direction is:

i-41c40fdc12e3d6cd186a8fdc4e419c3f-2010-05-27_la_te_xi_t_1_9.jpg

Increasing the time, decreases the acceleration. This is very similar to my “dangerous jumping calculator” – well, it is the same thing actually.

Comments

  1. #1 Patrick
    May 27, 2010

    Just a little FYI for you: They call it a tail-drop because he drops in off of his “normal riding back foot” (the “tail” of the board) as opposed to dropping in off of his “normal riding front foot” (the “nose” of the board). If he dropped in the other way it would be called a nose-drop. Skaters are also “regular” or “goofy-footed”. This guy is “regular” because his front foot is his left foot. The opposite would is true for “goofy-footers”.