At Newport Beach, CA, the long, straight shoreline separates the clear water (blue) from the sand (tan). Mitch, the lifeguard, is at M, 80 meters from the water, and sees a drowning child C, 120 meters from the sand. The points A and B are 280 meters apart along the shoreline. Mitch can run only 4 m/sec but he can swim 8 m/sec. At what spot on the shoreline AB should Mitch aim in order to reach the child at C as soon as possible? Compute the minimum time to the nearest tenth of a second; compare it to the times for the paths: MC, MAC, MBC.

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At Newport Beach, CA, the long, straight shoreline separates the clear water (blue) from the sand (tan). Mitch, the lifeguard, is at M, 80 meters from the water, and sees a drowning child C, 120 meters from the sand. The points A and B are 280 meters apart along the shoreline. Mitch can run only 4 m/sec but he can swim 8 m/sec. At what spot on the shoreline AB should Mitch aim in order to reach the child at C as soon as possible? Compute the minimum time to the nearest tenth of a second; compare it to the times for the paths: MC, MAC, MBC.

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