Question

macmilan learming 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 0.625 m / s. In still water, he can swim at 0.775 m/s. At what angle, less than 90°, with respect to the shoreline would you advise him to swim to travel directly across the stream to his campfire? ec Number The water is near freezing in temperature. Typically a human can only swim in such water for about 300 seconds (or 5 minutes) before hypothermia sets in. Calculate the time the explorer spends in the water if the river is 28.7 meters wide. wate secor r if the click to edit Number Based on your results, what would be your advice to the explorer? Approved. He'll get cold but he should be able to make it across. Sorry, but we will need to cancel the swim. He'll never make it across in time.

Answer 1

$\theta$ = angle = ?

v_s = velocity of the stream = 0.625 m/s

v_e = velocity of explorer in still water = 0.775 m/s

For the explorer to pass directly across the stream

v_e Cos$\theta$ = v_s

(0.775) Cos$\theta$ = 0.625

$\theta$ = 36.24 deg

w = width of the river = 28.7 m

t = time taken by explorer to cross the river

time taken is given as

t = w/(v_e Sin$\theta$)

t = 28.7/((0.775) Sin36.24)

t = 62.6 sec

Approved . he will get cold but he should be able to make it across