# Multivariable calc, boat moving on river functions problem

1. Feb 21, 2012

### mike1967

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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?

2. Feb 22, 2012

### tiny-tim

hi mike1967!
no it won't

start again!

3. Feb 22, 2012

### 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.

4. Feb 22, 2012

### tiny-tim

start by calling the angle "θ",

then find t from the x-component equation

5. Feb 22, 2012