Suppose a dog is sitting at point A= (1,0) in the plane, at the edge of a pool of water filling the unit disk x² +y <1. There is a treat sitting on the opposite side at point B= (-1,0). Wanting to get the treat as fast as possible, the dog runs some fraction of the way around the circle to some point C before getting impatient, jumping in and swimming straight for the treat. 2x (a) Now in general, suppose the dog runs at speed 1 and swims at speed v (with 0
Suppose a dog is sitting at point A= (1,0) in the plane, at the edge of a pool of water filling the unit disk x² +y <1. There is a treat sitting on the opposite side at point B= (-1,0). Wanting to get the treat as fast as possible, the dog runs some fraction of the way around the circle to some point C before getting impatient, jumping in and swimming straight for the treat. 2x (a) Now in general, suppose the dog runs at speed 1 and swims at speed v (with 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Suppose a dog is sitting at point A = (1,0) in the plane, at the edge of a pool of water filling
the unit disk x? +y <1. There is a treat sitting on the opposite side at point B = (-1,0).
Wanting to get the treat as fast as possible, the dog runs some fraction of the way around the
circle to some point C before getting impatient, jumping in and swimming straight for the
treat.
2x
B
A
(a)
Now in general, suppose the dog runs at speed 1 and swims at speed v (with 0 <v< 1).
What is the dog's fastest path to the treat? What is the slowest? I suggest you set this up
as a function of the angle x shown in the picture and use that the ZACB is a right angle.
Your answer will denend on v.
(b)
Does the answer surprise you? When v = 1, does it match your answer to part (a)? When
v = 0, does it match your answer to part (b)?
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