You are a member of a production crew filming a nature explorer in the Rocky Mou

Question

You are a member of a production crew filming a nature explorer in the Rocky Mountains. The explorer needs to swim across a river to his campsite. By watching debris flowing down the river, you estimate that the stream is flowing at 1.39 mph. In still water, he can swim at 1.63 mph. At what angle with respect to the shoreline would you advise him to swim to travel directly across the stream to his campfire?

The water is near freezing in temperature. Typically a human can only swim in such water for about 5 minutes before hypothermia sets in. Calculate the time the explorer spends in the water if the river is 88.9 feet wide.

Explanation / Answer

I. sin (theta) = u / v = 1.39 / 1.63 = 0.8675 = sin (60) nearly so, the angle with respect to shore = 90 + 60 = 150 degrees II. time of crossing the river t = d / square root of ( v^2 - u^2 ) = 0.0182 / square root of (2.28 - 1.72) = 0.02 hrs = 1.46 minutes III. with this speed he can safely cross the river. 1. Sin L = (1.39/1.63), Asin = 57.84 degrees upstream from straight across, or 32.15 degrees upstream relative to the bank. 2. Speed of swimmer straight across the river = sqrt. (1.63^2 - 1.39^2), = 0.725mph., = (5280 x .725) = 3,826.98ft/hr., or 63.788ft/min. (96.3/63.788) = 1.509 mins. 3. Advice 1 = you should make it OK. Advice 2 = Did you check whether there was crocodiles or pirhana in the river?

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