Relative velocity of perpendicular vectors

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Discussion Overview

The discussion revolves around the concept of relative velocity, particularly in the context of a boat moving across a river with a current. Participants explore how to determine the relative velocity of the boat with respect to the current and how this relates to other reference points, such as a stone floating in the water.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant suggests that the relative velocity of the boat with respect to the current could be understood as the speed at which it moves away from a stationary object in the water, like a stone.
  • Another participant clarifies the relationship between the velocities of the boat, the water, and the ground, proposing a formulaic approach to express this relationship.
  • A different participant expresses confusion about the concept of relative velocity, particularly in scenarios where the boat is moving with the current, questioning the meaningfulness of relative velocity in such cases.
  • There is a query about the specific data needed to calculate the boat's velocity with respect to the river's current and whether the boat's velocity is given relative to the ground or the water.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the interpretation of relative velocity in this context. There are multiple competing views and ongoing confusion regarding the application of the concept.

Contextual Notes

There are unresolved assumptions regarding the reference frames being used (ground vs. water) and the specific velocities involved, which may affect the understanding of relative velocity in this scenario.

BogMonkey
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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?
 
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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.
 
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.
 
BogMonkey said:
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.
 

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