A room has the dimensions 10 ft X 12 ft X 14 ft. A fly starting at one corner ends up at a diametrically opposite corner. (a) Find the displacement vector in a frame with coordinate axes parallel to the edges of the room. (b) What is the magnitude of the displacement? (c) Could the length of the path traveled by the fly be less than this distance? Greater than this distance? Equal to this distance? (d) If the fly walks rather than flies, what is the length of the shortest path it can take?

A room  has  the dimensions   10 ft X  12 ft  X  14 ft. A fly starting  at one  corner  ends  up  at a diametrically    opposite   corner. (a)  Find  the  displacement    vector  in  a frame  with  coordinate axes parallel  to the edges  of the room.  (b) What  is the magnitude  of  the  displacement?    (c)  Could   the  length   of  the  path traveled   by  the  fly  be  less  than  this  distance?   Greater   than this  distance?   Equal   to  this  distance?    (d)   If  the  fly  walks rather  than  flies, what  is the length  of the shortest  path  it can take?


1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
8 years ago
(c) The displacement vector of the fly defines the shortest distance between its starting point and the ending point, along the diagonal. Therefore, if the fly went along any other path, the distance travelled by her would be relatively larger. The maximum that the fly can do to save time is to travel along the displacement vector\overrightarrow{r} .
(d) The figure below shows the motion of the fly in the room:


Rounding off to two significant figures 236-234_1.PNG

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