There are several red lines because Elvis might have choosen to jump into the water at any distance from it. The red lines on the graph show the distance to the ball when swimming. When he does so, his closing velocity on the ball will be exactly his swimming speed, \( s \). At any point, Elvis can head straight toward the ball by swimming. This fact is unremarkable but it is very important. When Elvis does turn, he heads straight for the ball. Instead, Elvis turns into the water at some point before reaching C. To keep running down the beach, away from the ball, is so silly that it's unremarkable that a dog doesn't do it. From then on, Elvis is getting farther away from the ball. After running about three seconds, Elvis would run past the perpendicular point C. But then the closing velocity gets worse and worse. At first, running along the beach is a pretty good strategy and Elvis's closing velocity is fast. The graph shows that as Elvis runs down the beach, he gets closer to the ball. Then, as a function of time, Elvis's distance from the ball is Let \( y \) be Elvis's distance from the perpendicular point C. As Elvin runs along the beach, he's closing in on the ball. When should the student switch from job A to job B. She's working at a job that pays her at a certain rate, A. A student wants to earn enough money to pay her rent. So how is the dog finding a solution? If there's a method that works for a dog, perhaps the same method can work for a college student. Of course, Tim doesn't claim that even the dog of a mathematics professor can do calculus. Tim Pennings has famously described his dog Elvis's fetching behaviorĪs consistent with calculus. Dog Calculus is Really Economics Dog Calculus is Really Economics
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