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 0.677 m / s. In still water, he can swim at 0.763 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?

If we wish to cross the river in such a way that we reach directly opposite to the bank then in that case the velocity parallel to the flow of river must be ZERO

So here the let say he start his motion at some angle "theta" with the shore

So the velocity opposite to the flow of river must be same as the velocity of river so that it will cancel out

now here we can say

[tex]v cos\theta = v_r[/tex]

given that

v = 0.763 m/s

[tex]v_r = 0.677 m/s[/tex]

now from above equation

[tex]0.763 cos\theta = 0.677[/tex]

[tex]cos\theta = 0.887[/tex]

now the angle is given as

[tex]\theta = 27.5 degree[/tex]