Occasionally there are videos that are just perfect for a quick analysis. Above you can see a shot from the video in which Byron Jones breaks the record for standing long jump (I can’t embed the video, but you can watch it on youtube). Why is it a good video candidate for analysis? Here are a few reasons.

The camera is stationary. Yes, this makes it MUCH easier to analyze. It doesn’t zoom or pan either. Bonus.

The camera seems to be far enough away from the motion and it is viewing perpendicular to the motion of the jumper.

It isn’t just plain projectile motion. It’s not that there is anything wrong with projectile motion, but this is a bit more interesting in that the different parts of his body are moving differently.

As another bonus, this is a recent news item so that people are still talking about the Byron Jones jump. This makes it a great physics lesson that I can sneak into people’s lives.

Now for the analysis. Of course I will use Tacker Video Analysis (free and awesome) to get data from the video. I will skip all the details and just get to business. Since Jones isn’t a point mass, I need to mark different parts of his body. Just as an estimation, I marked the following points:

Head

Torso – I guessed at the center of mass of just his torso.

Arms – it would have been better to use two points for the arms (lower and upper) but I am lazy. I just estimated the center of mass for the two pieces of arms together.

Legs – same as the arms. One point for both parts of the legs.

Feet – I marked the bottom of the feet just so I could get data on when he left the ground and when he landed.

Now for the data. Here is what I get for the x-motion of the different parts.

Notice that after the human leaves the ground, the horizontal velocity is mostly constant (as it should be since there are no horizontal forces on the person). Also notice that the feet start off behind everything else (the rest of the body) but end up in the front. The long jump is measured based on your feet location, so this is a good thing to do. In case you aren’t aware, this data is in plotly so that you can see the data and make your own version of the graph if you like (this is one of the reasons that plotly is awesome). I usually save homework for the end of a post, but here is some now. If you take these 4 body parts (don’t use the feet) you can use them to find the x-location of the center of mass. How do you find the center of mass? Here is the formula. You already know the positions of the different body parts (from the graph), you just need to know the masses. Here is a publication that describes the human body mass distribution – that might be useful. Remember that there are two arms and two legs. Now for the vertical data:

That’s much more interesting than the x-direction. Notice that the only body part that seems to have a parabolic motion is the torso. If I fit a quadratic equation to part of the torso data (as you can see in the graph), I get a vertical acceleration of -10.62 m/s2. Remember that the vertical acceleration is twice the coefficient in front of the squared term (you can get a kinematics review in my intro ebook on physics – Just Enough Physics).

Vertical acceleration. But why is the vertical acceleration a little bit greater than g (-9.8 m/s2)? Well, this is just the acceleration of part of his body. As he is jumping, he is pulling his legs up. This means that his torso has to pull up on his legs such that the legs pull down on the torso. This extra downward force produces a greater downward acceleration.

Arms matter. Look at the motion of the arms compared to the motion of the feet. His arms are moving before his feet leave the ground. This means that his center of mass is also moving forward before he even “jumps”. This is why swinging your arms helps with the standing long jump. You should go outside and try the standing long jump. Do it with an normal arm swing and then try it with your arms at your side. Which way did you jump farther?

Jumping with weights. In fact, arm swing can be so useful that the ancient Greeks put weights in their hands to increase performance on the long jump – Weights gave Olympian long-jumpers a hand – Nature. By swinging the hand weight, a jumper can swing the weights forward during take off to increase launch speed. Then in, air the jumper can move the weights back to move the feet forward (the center of mass moves with a constant horizontal velocity).

Homework. Clearly there are many other cool things to look at. Here are some suggestions.