Four bugs sit at the comers of a square carpet L in. on a side. Simultaneously, each starts walking at the same rate of I in/sec toward the bug on its right See Fig. 1.3.9(a).
(a) Show that the bugs collide at the center of the carpet in exactly L sec.
(b) Using the result from (a). but using no calculus, tell how far each bug will travel.
(c) Use differential equations to find the paths of the bugs. Simplify the setup by starting the bugs at the four points (±1, 0) and (0, ± 1), malting L = ˆš2. Use Fig. 1.3.9(b) to deduce the relationship dr ‰ˆ -r dθ, for sufficiently small dθ.

Transcribed Image Text:

(r.eHT/2) (r,e)