Relative velocity of perpendicular vectors

In summary, the conversation discusses the concept of relative velocity and its application to a boat moving in a river with a current. The question is posed whether the boat's velocity with respect to the current is the same as its velocity with respect to the ground. The answer is yes, according to the formula provided. The conversation also considers the idea of relative velocity in a more abstract scenario and concludes that the river's velocity can be neglected in this case. The conversation also clarifies the terminology used, stating that the boat's velocity with respect to the current is the same as its velocity with respect to the water.
  • #1
BogMonkey
76
0
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 

FAQ: Relative velocity of perpendicular vectors

1. What is relative velocity?

Relative velocity refers to the velocity of an object relative to another object or reference point. It is the difference between the velocities of the two objects.

2. How is relative velocity calculated?

Relative velocity is calculated by finding the vector sum of the velocities of the two objects. This can be done by using the Pythagorean theorem and trigonometric functions to determine the magnitude and direction of the relative velocity.

3. What are perpendicular vectors?

Perpendicular vectors are two vectors that intersect at a 90 degree angle, also known as a right angle. This means that the two vectors are orthogonal to each other and do not share any common direction.

4. How is the relative velocity of perpendicular vectors calculated?

The relative velocity of perpendicular vectors can be calculated by taking the magnitude of one vector and multiplying it by the sine or cosine of the angle between the two vectors. This will give the component of the velocity that is perpendicular to the other vector.

5. Why is the relative velocity of perpendicular vectors important?

The relative velocity of perpendicular vectors is important in many fields, such as physics, engineering, and navigation. It allows us to understand and calculate the motion of objects in different directions and can help us predict the trajectory of objects in complex systems.

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