What is the shortest path a fly can take in a room with given dimensions?

[EngnrMatt]

Homework Statement

A room has dimensions 2.59 m (height) × 5.81 m × 6.09 m. A fly starting at one corner flies around, ending up at the diagonally opposite corner. (a) What is the magnitude of its displacement? (b) If the fly walks rather than flies, what is the length of the shortest path it can take? (Hint: This can be answered without calculus. The room is like a box. Unfold its walls to flatten them into a plane.)

Homework Equations

I'm thinking c=ab*sin(\phi) has something to do with it (cross product)

The Attempt at a Solution

I took the hint, but honestly I tried it several different ways before giving up. I have an absolutely terrible physics professor and even worse, the book is just as bad at explaining (Halliday and Resnick). I think that this has something to do with cross products of vectors though.

 

[jedishrfu]

Use the Pythagorean theorem in 3d to compute the box diagonal for the displacement.

For the other you have to try some paths like diagonally across the floor the up the wall or diagonally across a wall... There are a lot of possible walking paths.

 

[EngnrMatt]

Thanks, I didn't realize that pythagorean theorem worked in 3D. Just an example of one of those things that both my professor and the book fail to mention.

 

[SteamKing]

Your math professor should have told you about Pythagoras in 3D.

 

[vela]

Thanks, I didn't realize that pythagorean theorem worked in 3D. Just an example of one of those things that both my professor and the book fail to mention.

It's pretty easy to reason it out on your own. You should get used to the fact you're not going to be spoon-fed everything in college. Playing the victim card and blaming the book and professor for your difficulties is a sure-fire way to fail.