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A camera operator is 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, the operator estimates that the stream is flowing at 0.633 m/s0.633 m/s . In still water, the explorer can swim at 0.739 m/s0.739 m/s . At what angle, less than 90°, with respect to the shoreline should the operator advise him to swim so that he travels directly across the stream to his campfire?

Answer :

Answer:

31.06 deg

Explanation:

[tex]v_{s}[/tex] = speed of the stream = 0.633 m/s

[tex]v_{e}[/tex] = speed of the explorer = 0.739 m/s

[tex]\theta[/tex] = Angle with respect to shoreline

For the explorer to swim directly across the stream, necessary condition is

[tex]v_{e} Cos\theta = v_{s}[/tex]

[tex](0.739) Cos\theta = (0.633)[/tex]

[tex]Cos\theta = 0.8566[/tex]

[tex]\theta = Cos^{-1}(0.8566)[/tex]

[tex]\theta = 31.06[/tex]

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