Two bicyclists, starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1080 m due east and then turns due north and travels another 1430 m before reaching the campground. The second cyclist starts out by heading due north for 1950 m and then turns and heads directly toward the campground. (a) At the turning point, how far is the second cyclist from the campground? (b) In what direction (measured relative to due east) must the second cyclist head during the last part of the trip?

THE STRANGE NEW SCIENCE OF CHAOS ● Chaos = errors or deviations from expected results ○ Scientists try to minimize or eliminate it ● Linear system = the output is directly proportional to the input ● Examples of chaotic systems ○ Water bubbling down a stream ○ Smoke rising from a cigarette ○ Water dripping from a tap ○ The weather ○ Our nervous systems ● Chaotic systems are sensitive to initial conditions = a small change in the starting condition leads to a big change in the result ● Weather is hard to predict ○ The turbulent atmosphere cannot be described by simple linear equations ● Attractor = a preferred state towards which a chaotic system may tend ● Turbulence = much of the