You are not logged in.
Pages: 1
A cat sitting in a field suddenly sees a standing dog. To save its life, the cat runs away in a straight line with speed u. Without any delay, the dog starts with running with constant speed v>u to catch the cat. Initially, v is perpendicular to u and L is the initial separation between the two. If the dog always changes its direction so that it is always heading directly at the cat, find the time the dog takes to catch the cat in terms of v, u and L.
Offline
Please see my approach so far. I have used very small interval dt when cat has moved a distance of udt and dog vdt.
I am stuck with strange equation.
Thanks in advance
Last edited by pokrate (2012-11-25 03:23:48)
Offline
Hi;
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.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
Thanks for the links for enlightening me. Request you to take a look into this problem and lets together try to come up with some solution.
Offline
Hi;
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
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
Thanks again, but I will be extremely happy and will work on my own, if you or someone can just take a look at my approach to comment if it right or wrong ?
Offline
where s the separation between the animals at time t. (Note that the RHS is positive as
.) Suppose the dog catches the cat after time T. 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 have
Substituting the integral into the previous equation gives
Offline
Suppose at time t the dog is running at angle θ to the cat's direction of motion. The component of the cat's velocity parallel to that of the dog is ucosθ so the velocity of the dog relative to that of the cat iswhere s the separation between the animals at time t. (Note that the RHS is positive as
.) Suppose the dog catches the cat after time T. 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 have
Substituting the integral into the previous equation gives
This solution is copied from physicsforum website, and is non-calculus based, as integration is cancelled out.
Offline
If your approach is right, then why this approach is not right as shown in the image :
Offline
From which Physics Olympiad is this question ? I would really like to know
Offline
Hi;
See post #3 for similar problems.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
Pages: 1