- #1
Ackbach
Gold Member
MHB
- 4,155
- 89
Here's this week's problem.
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A dog sees a rabbit running in a straight line across an open field and gives chase. In a rectangular coordinate system, assume: A. The rabbit is at the origin and the dog is at the point $(0,L)$ at the instant the dog first sees the rabbit. B. The rabbit runs across the $x$-axis and the dog always runs straight for the rabbit. The dog runs twice as fast as the rabbit. Let $y=f(x)$ be the trajectory of the dog. Find $f(x)$ subject to the constraints that $y(0)=L$ and $\dot{x}(0)=0$. Where does the dog catch the rabbit?
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
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A dog sees a rabbit running in a straight line across an open field and gives chase. In a rectangular coordinate system, assume: A. The rabbit is at the origin and the dog is at the point $(0,L)$ at the instant the dog first sees the rabbit. B. The rabbit runs across the $x$-axis and the dog always runs straight for the rabbit. The dog runs twice as fast as the rabbit. Let $y=f(x)$ be the trajectory of the dog. Find $f(x)$ subject to the constraints that $y(0)=L$ and $\dot{x}(0)=0$. Where does the dog catch the rabbit?
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!