What is the formula for calculating the arclength of a general curve?

[sheepcountme]

Homework Statement

So here are the two pages of the project:
http://img.photobucket.com/albums/1003/aliceinunderwear/Calc2project1.jpg
http://img.photobucket.com/albums/1003/aliceinunderwear/Calc2project2.jpg

Homework Equations

Calc stuff, integrals in general. d=rt

The Attempt at a Solution

Anyways, I've figured out so far that I need the time that the boat arrives at the east gate first and in order to do this, I use d=rt where r is v.1 and x is the east position along the line. This will give me changing amounts for velocities so then I think I should just use excel and keep getting new velocity results until the boat reaches the east gate.

The prof more or less confirmed that I'm on the right track and he said that 'the hard part is over' however I'm stuck here.

First, I'm not sure how to calculate the distance the boat traveled along the river. I can figure out the point at which the river meets the east gate through graphing it and finding the intercept easy enough. And then from this I will have the distance the boy travels (pythagorean theorem), the time he needs to make that distance, and then can find his velocity.

So the part I'm missing really is how do I find the distance the boat traveled since it's not a straight line.

And then for the second part of the problem, how do I find the distance the boy has to run along the parabola?

Any help would be very much appreciated!

 

[gabbagabbahey]

So the part I'm missing really is how do I find the distance the boat traveled since it's not a straight line.

Don't you have some formula for calculating the arclength of a general curve $\textbf{r}(t)$?