***Having a hard time with questions 4-8 *****

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. A circle with three points, A, B, and C around its perimeter. Line segments are drawn between points A and B and between A and C. The angle formed at point A is shown as theta. (Section 4.7 in Calculus, Volume 1)

1. 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.

40/9(theta)+40/3cos(theta)

2. Find at what angle , in radians, the lifeguard should swim to reach the drowning person in the least amount of time

Derivative of theta= sin(^-1)(1/3)= 19.47

3. What is the domain of the function you created in part (a)?

[0,90)

4. How do you know that the function you created in Part I has a maximum and minimum value?

Derivative of theta is 19.47 which is minimum value

5. Discuss how your answers would be affected if the diameter of the pool increased.

That means the diameter would be larger therefore take longer for the person to reach the drowning victim

6. For what running speed would it be faster to swim the entire time? What angle would correspond to this scenario?
7. For what angle, , would it take the longest to reach the drowning person?
8. . Suppose the pool was rectangular. Respond to the following: Does it still make sense to parameterize using ?
9. 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.