# Homework Help: Magnitude of Displacement problem

1. Jan 29, 2012

### KrissyFivee

1. The problem statement, all variables and given/known data

A room has dimensions 3.15 m (height) 3.85 (width) m 4.10 (length) m. A fly starting at one corner flies around, ending up at the diagonally opposite corner.

(a) What is the magnitude of its displacement? (solved and got 6.45m)
(b) Could the length of its path be less than this magnitude?
(c) Could the length of its path be greater than this magnitude?
(d) Could the length of its path be equal to this magnitude?
(e) Take xyz axes so that the x axis is parallel to the width, the y axis is parallel to the length, and the z axis is parallel to the height. Express the components of the displacement vector.
(f) 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 the walls and flatten them into a plane.)

2. Relevant equations

|A| = sqrt(A^2+B^2+C^2)

3. The attempt at a solution

I don't even know where to begin with this problem . . .

So far all I've got is the displacement is 6.45m, which is correct.

2. Jan 29, 2012

### LawrenceC

Hint for b,c, and d:
The shortest distance between two points in space is a straight line.

For part e, I think the question is looking for the i,j,k components of the displacement vector so they are talking about a straight line. From the starting position, what are the components of the displacement.

For part f, sketch the box unfolded then eyeball the shortest path on the surface of the unfolded box. Determine its length by using a method like the one you used in part a.

3. Jan 29, 2012

### KrissyFivee

Thank you for the help :) I got it! I just didn't understand what the question was asking for!

4. Jan 29, 2012

Good!