5. You are starting a race on the beach at point A to reach a buoy at point B in the ocean, as pictured below (bird's eye view). A = (0,0) T(x) = -x + B = (b₁,b₂) You can run along the beach twice as fast as you can swim in the ocean. The aim is to find that the optimal location x to enter the ocean is such that 0 = 30°. Beach Ocean (a) Let v₁ = running speed and v₂ = swimming speed. Show that the total travel time between A and B is (explain your working): 1 VI V2 sin (= x √√(b₁-x)² + b². (b) Calculate T'(x). (c) Show that if v₁ = 2v2, the optimal angle to enter the ocean is 0 = 30°. Hint: Note that T(x) has no maximum (you can take arbitrary long detours) and that (b₁-x) (b₁-x)² + b²

5. You are starting a race on the beach at point A to reach a buoy at point B in the ocean, as pictured below (bird's eye view). A = (0,0) T(x) = -x + B = (b₁,b₂) You can run along the beach twice as fast as you can swim in the ocean. The aim is to find that the optimal location x to enter the ocean is such that 0 = 30°. Beach Ocean (a) Let v₁ = running speed and v₂ = swimming speed. Show that the total travel time between A and B is (explain your working): 1 VI V2 sin (= x √√(b₁-x)² + b². (b) Calculate T'(x). (c) Show that if v₁ = 2v2, the optimal angle to enter the ocean is 0 = 30°. Hint: Note that T(x) has no maximum (you can take arbitrary long detours) and that (b₁-x) (b₁-x)² + b²

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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