Suppose at timetthe dog is running at angleθto the cat's direction of motion. The component of the cat's velocity parallel to that of the dog isucosθso the velocity of the dog relative to that of the cat iswhere

.) Suppose the dog catches the cat after timesthe separation between the animals at timet. (Note that the RHS is positive asT. Integrating givesNow, the component of the dog's velocity parallel to that of the cat is

vcosθ, so when the dog catches the cat we haveSubstituting the integral into the previous equation gives

This solution is copied from physicsforum website, and is non-calculus based, as integration is cancelled out.

]]>Suppose at time

where *s* the separation between the animals at time *t*. (Note that the RHS is positive as

Now, the component of the dog's velocity parallel to that of the cat is *v*cos*θ*, so when the dog catches the cat we have

Substituting the integral into the previous equation gives

]]>Right now I am knee deep in several other problems as well as administrative matters. I already solved one of these before here, take a look at it

]]>Your problem is a pursuit curve.

http://mathworld.wolfram.com/PursuitCurve.html

http://curvebank.calstatela.edu/pursuit2/pursuit2.htm

google for more about pursuit curves. See if that helps you.

]]>I am stuck with strange equation.

Thanks in advance

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