Relative velocity of perpendicular vectors

[BogMonkey]

Using this diagram as an example
http://img25.imageshack.us/img25/231/diagramig.jpg
would I be right in assuming that the relative velocity of the boat with respect to the velocity of the current is the speed at which its moving away from say a stone floating down the river? In other words the resultant vector?

 

[Doc Al]

I think you mean:

Is the velocity of the boat with respect to the ground = the velocity of the boat with respect to the water + the velocity of the water with respect to the ground.

If that's what you mean, then yes.

 

[BogMonkey]

It didn't make any sense what I was describing there did it. What I was trying to describe was something more like the relative velocity of the river with respect to someone jumping over the river but the resultant vector in that case would be the opposite direction. What I'm really wondering is what's the boats velocity with respect to the rivers current? Since the boats moving with the rivers current is relative velocity between the two vectors in this case meaningless? I can see the image of the boat crossing the river in my head its just the idea of relative velocity that has me confused. I suppose in this case its no different than someone canoeing across a frozen river meaning the rivers velocity can be neglected.

 

[Doc Al]

What I'm really wondering is what's the boats velocity with respect to the rivers current?

You mean the boat's velocity with respect to the water? What data are you given? You gave the boat's velocity (in the y-direction). What was that respect to? The ground? Use the formula I gave--in words--in my last post.