So, One of my Students is a Pilot

It finally happened. The planets aligned, the stars shined with approval in the Western sky as night was chased away by day. We dropped some bags of flour from an airplane in physics today.

The build-up to this has been quite epic. We started planning it in August. We hit road blocks. Our pilot was to finish his coursework and recieve his license, but then the tragedy of delays and red tape struck. We languished in this limbo, jumping for physics problem to physics problem like drifters in box cars.

The goal here is narrative. We started studying acceleration and velocity, which led us to combining the two into the motion of objects as they fall. So often teachers get accolades simply for making things “fun.” I demand a little more than that; lots of things are fun, but I’d rather shoot for perplexing (thanks Dan), engaging–dare I say–riveting. There’s a reason kids play video games and watch movies instead of reading books and doing math problems: Narrative.

So, we call the FAA. We call the department of defense. We get clearance. We look up regulations.

We used Google Earth to find a suitable drop zone:

Click to embiggen.

We calculated how far the object will fall and where it will hit. See below.

We’re ready. The kids and I form a convoy and we drive out into the desolate, pre-winter that is December in Iowa.

Click to embiggen. Setting up the targets.

The co-pilot and I text message back and forth, and the drops begin:

Click to embiggen.

All-in-all, not the worst way to spend a frigid morning with 40 of my high schoolers.

Here’s the math:

The co-pilot planned to drop the bag when the plane was directly over the house in the drop zone. This is a great piece of physics, because most people naively believe that an object, once dropped, will fall straight down. When in fact the object will continue along horizontally as fast as it was originally going, while only picking up speed in the downward direction (hooray for gravity).

So, we needed to figure out how long it would take for the object to fall using the model for constantly accelerated motion (again, hooray for unbalanced gravity):

[latex size=3]h=\frac{1}{2}at^2[/latex]

h is height, a is acceleration, and t is time. The plane was 500 ft up, which is roughly 152.4 meters. The acceleration on Earth is 9.81 meters per second per second:

[latex size=3]d152.4m=\frac{1}{2}(9.81)t^2[/latex]

Solving for the time-to-fall yields:

[latex size=3]t=5.57s[/latex]

We agreed that the plane would fly at 90 mph (v = 40.23 m/s), so the distance d covered horizontally will be:

[latex size=3]d=vt[/latex]

[latex size=3]d=40.23m/s*5.57s[/latex]

[latex size=3]d=224m[/latex]

However, our bags did not hit at 224 meters, which gives my class a chance to really flesh out a model for drag and its effect on the trajectory of the bag; ho hum, yet another day planned out for me by the natural narrative of figure-stuff-out.

Solon physics students walking to the drop zone.