(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

See attached.

2. Relevant equations

3. The attempt at a solution

I originally began by assuming the rate was constant, obtaining the equations

[itex] V_x^2 + V_y^2 = 1[/itex]

[itex] \tan{\sigma} = \frac{V_y}{V_x} [/itex]

with the assumptions

[itex]V_x(\sigma) = f(\sigma)[/itex]

[itex]V_y(\sigma) = r + g(\sigma)[/itex]

and used the above equations to solve for f and g, and ended up getting the correct result for f, i.e.

[itex]f(\sigma) = \cos{\sigma}[/itex]

but did not get the right result for [itex]g(\sigma). [/itex]

Then I realize that the path was CURVED, hence there had to be acceleration involved, and upon reading other parts of the question figured out that we were not supposed to make the assumption that r was constant. i.e. it turns out

[itex]r = r(x)[/itex]

and I am unsure about how to deal with this to get the correct result

[itex]V_x(\sigma) = \cos{\sigma}[/itex]

[itex]V_y(\sigma) = r + \sin{\sigma}[/itex]

Any help would be greatly appreciated.

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# Velocity of boat in river with varying current

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