Multivariable calc, boat moving on river functions problem

[mike1967]

Homework Statement

there is a straight river 40m wide.
the water speed on the river can be expressed as the function f(x)=3sin(∏x/40)
If a boat is to cross the river from point a to point b at a constant velocity of 5 m/s determine the angle the boater should head.

Homework Equations

The Attempt at a Solution

it will take 8 seconds for the boater to cross the river.
I am thinking that since I am given that the river is 40m wide,
that I should integrate f(x) to find the distance the boater will have traveled after 8 seconds. then take the inverse tangent of (40/(∫f(x)|0->8?) to find the angle?

 

[tiny-tim]

hi mike1967!

there is a straight river 40m wide.
…
If a boat is to cross the river from point a to point b at a constant velocity of 5 m/s determine the angle the boater should head.
…
it will take 8 seconds for the boater to cross the river.

no it won't

start again! ​

 

[mike1967]

I'm not sure where to start then. I figured t=8 because v(t)=5 to x(t)=5t 40=5t 8=t.

 

[tiny-tim]

start by calling the angle "θ",

then find t from the x-component equation ​

 

[mike1967]

https://plus.google.com/photos/105869685778449284705/albums/5712068745170213361

rethought it, thank you.
Does this look more right?
Then integrate with respect to t. solve at ∫f(0) for alpha?