## the beach raceA beach race begins from a point, 4 km out to sea from one end of a 10km beach. Racers must swim to a point along the beach, and then run to the finish line. If I can swim at 4 kph and run at 10 kph, to what point on the beach should I aim to land? Can you find the landing point for which the time of the race will be as short as possible - as accurately as possible? **Drag point C to find the landing position which will result in the LONGEST time for the race.****There are two landing points which will result in a race time of exactly 2 hours. One of these is to swim directly to the point O and then run the full length of the beach (swimming the shortest possible distance). Drag the point C to find the other landing point which will result in a 2 hour race.****Now build an algebraic model for the times for the race, letting the distance OC = x:****Finally, plot the derivative of this RaceTime(x) function to locate the best place to land:**
Steve Arnold, with thanks to Mike May S.J. for his JavaScripting. 24/03/2008, Created with GeoGebra |

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