Dunking On The Moon

Blake Griffin has been throwing down emphatic dunks all across the NBA, soaring high above the 10 foot rim. Many people might wonder how high Griffin could actually dunk, but I'll go a small step (or maybe a giant leap) beyond in the spirit of applying for a SpaceX internship. How high could Griffin dunk on the moon? And who would be the highest dunker?

It's not actually very complicated physics, just use M*G*H (conservation of energy), and M (for mass) doesn't actually matter here because it's the same for a player on the moon. With gravity (G) on the moon roughly 1/6 of earth gravity, just multiply an earth vertical (H) by 6 to get a moon vertical. Here's what happens with some of Earth's best basketball players:

Player	Height	Vert	Earth	Moon
Yao Ming	7'6"	21	10'11"	19'9"
Austin Link	6'4"	24	9'11"	20'0"
Blake Griffin	6'10"	35.5	11'3"	26'2"
Nate Robinson	5'9"	43.5	10'9"	29'0"
Jamario Moon	6'8"	43	11'8"	29'9"
Michael Jordan	6'6"	48	12'4"	32'6"
Kadour Ziani	5'10"	60	12'0"	37'3"

Even I could dunk on a 20 foot hoop on the moon, despite inconsistency on the earth. It's also striking how much more important jumping ability is on the moon. All of a sudden I can out dunk Yao Ming, and Nate Robinson has almost 3 feet on Blake Griffin. The aptly named Jamario Moon and Michael Jordan can of course hold their own (MJ based off his probably inflated vertical may be the best earth dunker) but the title of best moon dunker probably goes to the man with the highest vertical on earth, Kadour Ziani. Of course, he already makes his living as a professional dunker, so he may not even need the moon. But with it, he'd outshine even the brightest of NBA stars.

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.