Question

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 1

31.06 deg

Step-by-step explanation:

`v_(s)` = speed of the stream = 0.633 m/s

`v_(e)` = speed of the explorer = 0.739 m/s

`\theta` = Angle with respect to shoreline

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

`v_(e) Cos\theta = v_(s)`

`(0.739) Cos\theta = (0.633)`

`Cos\theta = 0.8566`

`\theta = Cos^(-1)(0.8566)`

`\theta = 31.06`