Watch a Harlem Globetrotter Sink a Shot from a Plane

Author: Rhett Allain / Source: WIRED

Oh, you think you are pretty awesome with the basketball trick shots? Well, maybe you are—but can you score with a shot from an airplane as it flies by? That’s what we have here with the Harlem Globetrotters (although it seems like Dude Perfect might have done this too).

For me, this is a classic physics problem. If you open up your introductory physics textbook you will find a problem just like this. I promise it’s there. It looks something like this:

A pilot needs to fly by and drop a package to a human (feel free to add your own back story). The plane flies at an altitude of 10 meters with a speed of 20 m/s. At what horizontal distance before the drop location should the package be dropped?

Here is a diagram to go with the problem.

If you are a Harlem Globetrotter, you can replace the target with a basketball hoop.

Physics Solution

Now let’s solve this problem.

I’ll be straightforward with you—this is really just a projectile motion problem. Once the ball leaves the plane, there is basically just one force acting on it—the gravitational force pulling straight down. This gives the ball a vertical acceleration of 9.8 m/s² and constant horizontal velocity. That is pretty much the definition of projectile motion. But what about air resistance? Yes, that might have a small effect, but I will leave the investigation of air resistance as a homework problem for you (at the the end).

Now for the secret to projectile motion problems. (Be sure to keep this secret safe.) For a projectile motion problem, you really have two separate kinematics problems. In the horizontal direction, you have a constant velocity problem and in the vertical direction you have a constant acceleration problem. These two motions (in the x and y-directions) are independent except for the time it takes.

This means that I can take one direction (let’s say the y-direction) and solve for the time it takes to move. I can then use that same time for the x-direction and find something useful. That’s exactly what I’m going to do. There will be some math, so prepare yourselves. Also, I’m going to solve this without putting any values in (like height and stuff) until the end—that’s the physics way.

Here is what I have to start with.

• 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)

So, like I…

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