4. A lifeguard is standing on the beach 15 meters from the water when she spots a nonswimmer 15 meters from shore in need of rescuing. Unfor- tunately, she is 100 meters down the beach from the swimmer, and all of her "reach/throw/row" equipment is being used; she decides to run across the beach and make a dangerous swimming rescue ("go"). Her top running speed in the sand is 5 m/s, and her top swimming speed is 2 m/s. (a) Suppose that the life- guard runs diagonally to a point on the shore perpendicular to the nonswimmer, and then enters the water and swims 15 m. How long will it take her to make contact? (b) Suppose that the lifeguard runs 15 m directly to the water, and then swims diagonally to the nonswimmer. How long will the trip take for this path? (c) Suppose that the lifeguard chooses to run shore along one diagonal, and swim to the nonswimmer along another diagonal. Find, by trial and error using your calculator, or otherwise, the two diagonals that will give the shortest total time, and calculate the time.
4. A lifeguard is standing on the beach 15 meters from the water when she spots a nonswimmer 15 meters from shore in need of rescuing. Unfor- tunately, she is 100 meters down the beach from the swimmer, and all of her "reach/throw/row" equipment is being used; she decides to run across the beach and make a dangerous swimming rescue ("go"). Her top running speed in the sand is 5 m/s, and her top swimming speed is 2 m/s. (a) Suppose that the life- guard runs diagonally to a point on the shore perpendicular to the nonswimmer, and then enters the water and swims 15 m. How long will it take her to make contact? (b) Suppose that the lifeguard runs 15 m directly to the water, and then swims diagonally to the nonswimmer. How long will the trip take for this path? (c) Suppose that the lifeguard chooses to run shore along one diagonal, and swim to the nonswimmer along another diagonal. Find, by trial and error using your calculator, or otherwise, the two diagonals that will give the shortest total time, and calculate the time.
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Transcribed Image Text:4. A lifeguard is standing on the beach 15 meters from the water when
she spots a nonswimmer 15 meters from shore in need of rescuing. Unfor-
tunately, she is 100 meters down the beach from the swimmer, and all of her
"reach/throw/row" equipment is being used; she decides to run across the beach
and make a dangerous swimming rescue ("go"). Her top running speed in the
sand is 5 m/s, and her top swimming speed is 2 m/s. (a) Suppose that the life-
guard runs diagonally to a point on the shore perpendicular to the nonswimmer,
and then enters the water and swims 15 m. How long will it take her to make
contact? (b) Suppose that the lifeguard runs 15 m directly to the water, and
then swims diagonally to the nonswimmer. How long will the trip take for this
path? (c) Suppose that the lifeguard chooses to run shore along one diagonal,
and swim to the nonswimmer along another diagonal. Find, by trial and error
using your calculator, or otherwise, the two diagonals that will give the shortest
total time, and calculate the time.
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