PHY183-Lecture8

# PHY183-Lecture8 - Aquathlon(1 The Aquathlon consists of two...

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January 26, 2006 1 Engineers 1 Spring Semester 2006 Lecture 8 January 26, 2006 2 Aquathlon Aquathlon (1) (1) ! The Aquathlon consists of two legs, a swim (distance b) followed by a run (distance a). a = 3 km, b = 1.5 km ! The athletes swim with a speed v 1 = 3.5 km/h and run with a speed v 2 = 14 km/h Which angle ! will result in the shortest finish time? ! 1) Red dashed line: shortest distance between start and finish a 2 + b 2 = 1.5 2 + 3 2 km = 3.354 km January 26, 2006 3 3) Arbitrary path between those two extremes: characterized by angle ! Swim a distance of and then run a distance of ! The total time is Aquathlon(2) Aquathlon(2) Corresponding time t red = a 2 + b 2 / v 1 = (3.354 km)/(3.5 km/h) = 0.958 h a 1 2 + b 2 a 2 2) Swim straight to shore and then run t blue = b v 1 + a v 2 = 1.5 km 3.5 km/h + 3km 14 km/h = 0.643h t ( " ) = a 1 2 + b 2 v 1 + a 2 v 2 = b v 1 cos + a # a 1 v 2 = b v 1 cos + a # b tan v 2 January 26, 2006 4 Aquathlon(3) Aquathlon(3) t ( ) = b v 1 cos + a # b tan v 2

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January 26, 2006 5 Aquathlon Aquathlon (4) (4) ! To find the minimum time
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PHY183-Lecture8 - Aquathlon(1 The Aquathlon consists of two...

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