Register to reply

DE problem: Dog chasing a rabbit

by camilus
Tags: chasing, rabbit
Share this thread:
tdude
#19
Oct27-10, 10:40 PM
P: 4
Could someone also derive the equation in relation to y?

I'm having huge problems with a question of the sort. Hopefully with the steps laid out it would become clear. Thanks!
corey2014
#20
Apr16-12, 07:45 PM
P: 22
So how would I do this if the rabbit has 1/2 the velocity? how would i set up an equation for how X, and Y will change?
HallsofIvy
#21
Apr17-12, 08:52 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,304
Quote Quote by Defennder View Post
v is a function of t, and x is also a function of t. Doesn't this mean that v can be regarded as a function of x?
Well, yes. A constant function for this problem.
ppoundstone
#22
May1-14, 12:54 AM
P: 1
Here's another approach that doesn't assume that the dog and rabbit run at constant speeds (but their speeds are the same).

Suppose that after some time t>0 the dog has arrived at the point (x,y) and the rabbit has arrived at the point (0,r). Then the distance the dog has travelled is given by
[itex]\int^{L}_{x}[/itex][itex]\sqrt{1+(dy/du)^2}du[/itex] and the distance the rabbit has travelled is r. Since they are traveling at the same speed we then have that

r=[itex]\int^{L}_{x}[/itex][itex]\sqrt{1+(dy/du)^2}du[/itex].

Now, since the dog is heading straight towards the rabbit, we have that dy/dx = (y-r)/x, and so r=y-x(dy/dx), implying that

y-x(dy/dx)=[itex]\int^{L}_{x}[/itex][itex]\sqrt{1+(dy/du)^2}du[/itex].

Differentiating both sides with respect to x gives the differential equation in part a.
HomogenousCow
#23
May1-14, 02:17 AM
P: 356
R(t) denotes the position of the rabbit. It works even if either speeds are not constant.
That minus sign is because I forgot to throw a plus/minus in front of the square root.
Attached Thumbnails
gfhfghf.PNG  
HomogenousCow
#24
May1-14, 02:34 AM
P: 356
oooh..the next part is nice.
Interesting problem.


Register to reply

Related Discussions
Rabbit + rat =? General Discussion 22
Down The Rabbit Hole...? General Discussion 6
Rabbit family problem. General Math 2
Chasing Cars Problem! Advanced Physics Homework 1
Chasing Problem Calculus 6