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DE problem: Dog chasing a rabbit

by camilus
Tags: chasing, rabbit
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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!
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?
Apr17-12, 08:52 AM
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PF Gold
P: 39,338
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.
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


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


Differentiating both sides with respect to x gives the differential equation in part a.
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.
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May1-14, 02:34 AM
P: 356
oooh..the next part is nice.
Interesting problem.

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