Question
I need help with Part 2, Part 1 is given for context Part I: Complete the following steps: Reference: https://openstax.org/books/calculus-volume-1/pages/4-7-applied-optimization-problems Question 327 A lifeguard is
I need help with Part 2, Part 1 is given for context
Part I: Complete the following steps:
Reference: https://openstax.org/books/calculus-volume-1/pages/4-7-applied-optimization-problems
Question 327
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, expressed in radians.
- Find at what angle , in radians, the lifeguard should swim to reach the drowning person in the least amount of time.
Part II: Based on your work in Part I, discuss the following:
- Suppose the pool was rectangular. Respond to the following:
- Does it still make sense to parameterize using? Why or why not?
- If not, what parameter would you use?
- If so, how does the parameterization change?
- Set up, but do not solve, this problem with a rectangular pool.
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