How would I solve for part 2?

Question

Consider a lifeguard at a circular pool with diameter 43 meters. The lifeguard, at position AA, must reach someone who is drowning on the exact opposite side of the pool, at position CC. The lifeguard swims at a rate of 1.76 m/s and runs at a rate of 3.07 m/s.

Part 1: Find a function T, that measures the total amount of time it takes to reach the drowning person as a function of the swim angel theta?

CORRECT ANSWER I GOT: (43cos(theta)/1.22)+(43(theta)/3.26)

Part 2: HELP

At what angle theta should the lifeguard swim to reach the drowning person in the least amount of time?

Answer 1

°I do not understand your answer to Part 1, but given that,

this is how you do Part 2.

Minimum of the function T occurs either at end of your valid interval,

or at a local extremum, i.e.,where the derivative is 0.

One end of the valid interval corresponds to him running all the way,

and the other corresponds to him swimming all the way.

You can simply evaluate your function at those two points and then

compare with the local extremum obtained next.

We set the derivative T'(theta) = 0:

(-43sin(theta)/1.22) + (43/3.26) = 0

sin(theta) = 1.22/3.26 = 0.3742

theta = 22°

The last step is to compare the time for theta = 22° with the other

two candidates.