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You are not logged in. #1 20121126 01:40:34
Physics olympiad questionA 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. #3 20121126 03:27:38
Re: Physics olympiad questionHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20121126 04:19:41
Re: Physics olympiad questionHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20121126 18:48:00
Re: Physics olympiad questionSuppose 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 is 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 gives Now, 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 #8 20121126 20:22:28
Re: Physics olympiad question
This solution is copied from physicsforum website, and is noncalculus based, as integration is cancelled out. 