Friday, October 22, 2010

Physics of Sports- Jump Balls

As a physics major, I thought it might be interesting to introduce some physics concepts. Also, I have the sweet picture above which needed to make it in here. That fool in red in the middle is me, clearly getting skied on by second team All-American and player of the year candidate Nneka Ogwumike.
The weird thing about this photo though, is that I actually won the tip. It should be a pretty even match, my 6'4" height and 24 inch vertical against her 6'2" and 30. This particular tip went my way though because I timed my jump better, she went up to early, and is already going down in this picture as I'm going up. Fortunately, thanks to physics, I knew when to time my jump:
Beware, this makes heavy use of one equation: 4.9*t^2 = x where t is time from stop and x is distance object has fallen. Hopefully I have derived it right, or else I've made myself a fool for all the internet to see.

Say the ball is thrown about 13 feet in the air (a reasonable estimate). Being my height, with my ups (which aren't quite as high when there's somebody jumping against you) I would probably best tip the ball at around 10 feet plus a few inches off the ground so I can get a solid touch on it. To jump two feet off the ground would take .35 seconds:
4.9*t^2 = .6 meters, t = .35 seconds
For the ball to drop those 3 feet from it's apex takes .41 seconds:
4.9*t^2 = .82 meters, t = .41 seconds
That means to time the jump, I have to leave .06 seconds after the ball reaches the top, or when it's 1.8 centimeters below the top.
4.9*.06^2 = x, x = .018 meters = 1.8 cm
Given that when already in position, it takes about .2 seconds to go from deciding to jump to actually leaving the ground, I actually want to try to jump .14 seconds before the ball peaks. That's 9.6 cm below the top (you know the equation by now). Any before that and I'll fall before I get to the ball. Any after that, and I won't get the ball at my peak.
So with a little help from physics, I won the tip. Then I returned to my usual duties of taking elbows in the gut for the sake of Stanford Women's Basketball. While wearing my new free basketball shoes of course.

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