posted by hannah .
A room has dimensions 3.00 m (height) 3.70 m 4.30 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) Could the length of its path be less than this magnitude? (c) Greater than this magnitude? (d) Equal to this magnitude? (e) Choose a suitable coordinate system and express the components of the displacement vector in that system in unit-vector notation. (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 its walls to flatten them into a plane.)
(a) If one corner is on the ceiling and the opposite corner is on the floor, the straight-line distance between them is
sqrt (a^2 + b^2 + c^2) = 6.417 m
(b) How could it?
(c) Suppose it did not fly in a straight line. Then what?
(d) Can the magnitude equal the magnitude? Does 2 = 2?
(e) 2.00i + 3.70 j + 4.30 k
(f) Take the hint. There are two possible short routes to the far corner; the path length depends upon which nonadjacent wall the fly walks to first.
One route gives a minimum length of
sqrt[(4.3+3)^2 +3.7^2] = 8.18 m
and the other has a minimum length of
sqrt[(3.7+3)^2 +4.3^2] = 7.96 m