What is the Shortest Path for a Fly to Walk Around a Room?

[goaliejoe35]

Homework Statement

A room has dimensions 2.22 m (height) × 5.64 m × 6.15 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.)

The Attempt at a Solution

For Part A I simply found the displacement...

sqrt[(2.22)^2+(5.64)^2+(6.15)^2] = 8.63484 m

Part B is what i don't understand. Wouldn't the shortest path be diagonally across the room? so I tried pythagorean theorem a^2+b^2=c^2

(5.64^2+(6.15)^2=c^2
c=8.345
However this is not the correct answer. I am also confused by the hint that says to unfold the walls like a box, I don't see what that has to do with anything.

Could someone please try to help me with Part B?

 

[tiny-tim]

Hi goaliejoe35!

I think it means the fly walks from, say, the bottom-south-east corner to the top-north-west corner.

So it has to walk along two walls, or the floor and one wall.

I don't know how to explain the box thing … I can only suggest you get an actual box, and try it!

 

[Kurdt]

If you're familiar with the net of a solid object then what it means by unfold the room is find its net. Then draw a straight line from what will be one corner of the room to the opposite corner and work out the distance.