A lifeguard is at point A of a circular pool with diameter 40 m. He must reach someone who is drowning on the exact opposite side of the pool, at position C. The lifeguard swims with a speed v = 3 m/s from point A to point B, and then runs around the pool from point B to point C at speed w = 9 m/s.Find a function that measures the total amount of time it takes to reach the drowning person as a function of the swim angle, θ expressed in radians.Find at what angle θ, in radians, the lifeguard should swim to reach the drowning person in the least amount of time.What is the domain of the function you created in part (a)?Please give as much detail as you can, It helps me learn / I am trying to learn.Please and thank you! A0BC

Answered: A lifeguard is at point A of a circular…

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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A lifeguard is at point A of a circular pool with diameter 40 m. He must reach someone who is drowning on the exact opposite side of the pool, at position C. The lifeguard swims with a speed v = 3 m/s from point A to point B, and then runs around the pool from point B to point C at speed w = 9 m/s.

Find a function that measures the total amount of time it takes to reach the drowning person as a function of the swim angle, θ expressed in radians.
Find at what angle θ, in radians, the lifeguard should swim to reach the drowning person in the least amount of time.
What is the domain of the function you created in part (a)?

Please give as much detail as you can, It helps me learn / I am trying to learn.

Please and thank you!