Introductory Vector Equation Illustrated by a Moving River - Picture Included

In summary, the problem involves a swimmer trying to cross a river from point A to point B. The distance from A to C is 100 meters and from C to B is 75 meters. The current in the river is 5 meters per second and the swimmer's velocity relative to the water makes an angle with the line from A to C. The question is what speed, relative to the water, should the swimmer have to swim directly from A to B.
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Introductory Vector Equation Illustrated by a Moving River -- Picture Included

Homework Statement


A swimmer wants to cross a river, from point A to point B, as shown in the figure. The distance (from A to C) is 100 , the distance (from C to B) is 75 , and the speed of the current in the river is 5 . Suppose that the swimmer's velocity relative to the water makes an angle of with the line from A to C, as indicated in the figure.
5Agg2.jpg
To swim directly from A to B, what speed , relative to the water, should the swimmer have?

Homework Equations



A to B2=1002+752

A to B= 125 meters

That's about all I really know how to do. For some reason I can't think of a way to go about solving this problem. Any ideas?
 
Last edited:
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  • #2


What's the question?
 
  • #3


ideasrule said:
What's the question?

That's embarrassing, can't believe I left that out. The question is now included.
 
  • #4


Hmm, I've looked through all the related threads, however, in all instances the problem is similar a solution is available but documentation showing how the solution is reached is unavailable. I'm much more interested in the necessary steps to solve this problem than the actual solution.
 

1. What is a vector equation?

A vector equation is an equation that uses vectors to represent mathematical quantities that have both magnitude and direction. It is typically written in the form of a linear combination of vectors, where each vector is multiplied by a scalar coefficient.

2. How is a vector equation illustrated by a moving river?

In the context of a moving river, a vector equation can be used to represent the velocity of the river's flow. The magnitude of the vector would represent the speed of the river, while the direction would represent the direction of the flow.

3. What is the significance of using a vector equation to represent a moving river?

Using a vector equation allows us to mathematically model the motion of the river, which can help us better understand and predict its behavior. It also allows us to easily manipulate and analyze the river's flow, such as calculating its speed at different points or determining the direction of its flow.

4. Can a vector equation be used to represent other physical phenomena?

Yes, a vector equation can be used to represent a wide range of physical phenomena, including but not limited to, motion, force, acceleration, and electric and magnetic fields. It is a powerful tool that is widely used in various fields of science and engineering.

5. How is a vector equation different from a scalar equation?

A scalar equation only involves quantities that have magnitude, such as temperature or mass, while a vector equation also takes into account the direction of the quantity. Scalar equations are one-dimensional, while vector equations are multi-dimensional, making them more complex but also more versatile in their applications.

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