Vector addition, trying to find the angle

  • #1
Ineedhelpwithphysics
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7
Homework Statement
IN picture
Relevant Equations
Addition of angles
Is angle Vag 180 since the vector is a straight line pointing left?
Also you can add 30 degrees with 150 which will be 180?

1697737028016.png
 
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  • #2
Yes, the wind velocity vector forms an angle of 180° with the positive x-axis.
Adding 30 degrees to 150 degrees will always give you 180 degrees, but that is not the angle that the resultant you are looking for forms relative to the positive x-axis.

By the way, "Addition of angles" is not an equation.
 
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  • #3
Ineedhelpwithphysics said:
Also you can add 30 degrees with 150 which will be 180?
How is this relevant to solving the problem? Just because you can combine two numbers given in the problem to produce a third doesn't mean you should do it. You need to have a valid reason for doing so.

When it comes to vector addition, you have three basic building blocks. First, you can resolve a vector into components. If a vector ##\vec A## has magnitude ##A## and direction ##\theta## (relative to the +x axis), its components are ##A_x = A \cos\theta## and ##A_y = A \sin\theta##. Second, you can go the other way: if you know the components of a vector, its magnitude is ##A = \sqrt{A_x^2 + A_y^2}## and its direction satisfies ##\tan \theta = A_y/A_x##. Finally, you have the rule about how to actually add the vectors: if ##\vec C = \vec A + \vec B##, then ##C_x = A_x + B_x## and ##C_y = A_y + B_y##.

Using just those building blocks, can you come up with a way to use them to solve the problem at hand?
 
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FAQ: Vector addition, trying to find the angle

1. What is vector addition?

Vector addition is the process of combining two or more vectors to produce a resultant vector. This involves adding the corresponding components of the vectors, often using geometric or algebraic methods.

2. How do you find the angle between two vectors?

To find the angle between two vectors, you can use the dot product formula: \( \mathbf{A} \cdot \mathbf{B} = |\mathbf{A}| |\mathbf{B}| \cos(\theta) \). Rearrange this to solve for the angle \( \theta \): \( \theta = \cos^{-1} \left( \frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{A}| |\mathbf{B}|} \right) \).

3. What is the resultant vector?

The resultant vector is the vector obtained by adding two or more vectors. It represents the combined effect of the original vectors. For vectors \( \mathbf{A} \) and \( \mathbf{B} \), the resultant vector \( \mathbf{R} \) is \( \mathbf{R} = \mathbf{A} + \mathbf{B} \).

4. How do you add vectors geometrically?

Geometrically, vectors are added using the tip-to-tail method. Place the tail of the second vector at the tip of the first vector. The resultant vector is drawn from the tail of the first vector to the tip of the second vector. This can also be visualized using the parallelogram method.

5. How do you use components to add vectors?

To add vectors using components, break each vector into its horizontal (x) and vertical (y) components. Add the corresponding components separately: \( \mathbf{R}_x = \mathbf{A}_x + \mathbf{B}_x \) and \( \mathbf{R}_y = \mathbf{A}_y + \mathbf{B}_y \). The resultant vector \( \mathbf{R} \) can then be found using \( \mathbf{R} = \sqrt{\mathbf{R}_x^2 + \mathbf{R}_y^2} \) and the angle \( \theta \) using \( \theta = \tan^{-1} \left( \frac{\mathbf{R}_y}{\mathbf{R}_x} \right) \).

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