If you spend much time online, you’ve probably seen the tweet from the Harlem Globetrotters last week in which Bull Bullard sinks a shot from a Piper Cub airplane.
Wired today looks at this in slow motion.
Let’s go to the videotape.
Initial horizontal x-velocity = v0 (the object is moving with the same horizontal speed as the plane)
Initial x-position = 0 (starts at the origin)
Final x-position = x (just going to call it x like in the diagram)
Initial vertical velocity = 0 (initial not moving in the y-direction)
Initial y-position = h
Final y-position = 0 (calling the ground y = 0)
There’s nothing better than the intersection of sports and physics.
I’m going to guess that this plane is going about as slow as it can go. The stall speed of a Piper Cub is about 38 mph so I will use a starting velocity that’s a little bit faster—let’s call it 20 m/s. A standard basketball hoop is 3.05 meters—so let’s say the plane is twice this height at 6.1 meters. Putting these values into the solution above gives an horizontal distance of 22.3 meters. That is the point that you should let go of the ball.
We cannot allow the wizadry of math to take away from Bullard’s shot, of course, because most of the above is an assumption.
A plane’s speed, for example, is airspeed, which is not the same as groundspeed because the plane is moving in the air mass which is also moving.
Also, while the stall speed of a plane remains relatively constant in level flight, the true air speed at which it stalls changes with altitude and temperature.
Nonetheless, Rhett Allain, an associate professor of physics at Southeastern Louisiana University, does a great job making the relevance connection between math and “real life,” inviting readers even to calculate how big the “window” is for releasing the ball and still make the shot.
But could a non-basketball-playing person make the same shot armed with only the physical calculations to make it?
Science says yes. But it is easier to explain why a shot went in the basket than to actually make it go in.