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I read recently that if I'm in a plane that hits turbulence, the plane might only move 1 to 20ft. However, due to the speed that plane is travelling at (say cruising at 550mph). The passengers in the plane will accelerate and move a distance greater than the plane has moved.

Ignoring how bad that example may be. How would you determine the relationship between the displacement and speed of a plane and the displacement and speed of the items inside?

The same could be applied to a box you're holding in your hand that contains some smaller items. If I was to move the box up 3 inches at a slow speed, I would not expect the items to move (relative to the box), but if I did it quickly, I would expect them to hit the roof of the box, but how could I calculate that?

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  • $\begingroup$ Someone modified this as 'homework and exercises' even though I'm doing research to tackle my fear of flying haha! $\endgroup$ – Matthew Haworth Apr 17 '18 at 10:44
  • $\begingroup$ Yes, the HW&exercises tag is not exclusively for HW questions - but for the style of homework questions. This may not be your homework but it could well be someone elses $\endgroup$ – Alex Robinson Apr 17 '18 at 12:19
  • $\begingroup$ I've hit the ceiling before (with the seat belt on): always want to know how much the plane moved. The wings were flexing about 5-10' under the aero-load. PS: everyone was freaking out. Oh, and use your iPhone accelerometer. $\endgroup$ – JEB Apr 17 '18 at 13:37
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If I was to move the box up 3 inches at a slow speed, I would not expect the items to move

I would expect them to move. Three inches.

but if I did it quickly, I would expect them to hit the roof of the box

Only because you stopped moving the box. It's the box that's doing something strange, stopping suddenly it mid-flight, not the stuff inside.

How far they would move relative to the box is simply d = v^2/2g where v is the initial velocity (upward of the box) and g is the acceleration of gravity. Modify that by the non-instant stopping of the box.

The real problem here is finding v. Modern airplanes have very flexible wings specifically to damp out these motions. Add the foam of the seat and your butt and you have a very difficult practical problem.

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  • $\begingroup$ Sorry, I should have qualified that I meant 'relative to the box'. Thanks for your answer! $\endgroup$ – Matthew Haworth Apr 17 '18 at 12:41

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