Vectors, magitude, scalar components

In summary, the displacement vectors A, B, and C are given with their corresponding scalar components and magnitudes. To determine which two vectors are equal, we can compare their magnitudes. It is given that vector A and vector C have the same magnitude of 100.0 m, and to support this choice, we can calculate that both vectors are directed at an angle of 36.9 degrees above the + x axis. Therefore, vector A and vector C are the two equal vectors.
  • #1
brittbc
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Homework Statement



the displacement vector A has scalr omponents of Ax= 80.0 m and Ay= 60.0 m. the displacement vector B has a scalr component Bx= 60.0 m and a magnitude of B=75.0m. The displacement vecto C has a magnitude of C= 100.0 m and is directed at an angle of 36.9 degrees above the + x axis. Two of these vectors are equal. determine which two, and support your choice with a calculation.

Homework Equations




The Attempt at a Solution


vector A= 100m
By= 45m
vector A= vector C
 
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  • #2
So vector A and vector C have the same magnitude. Can you show they're both 36.9 degrees above the x-axis.
 
  • #3


The two vectors that are equal are A and C. This can be determined by calculating the magnitude of vector A using the Pythagorean theorem: A = √(Ax^2 + Ay^2) = √(80.0m^2 + 60.0m^2) = √(6400m^2 + 3600m^2) = √10000m^2 = 100m. This is the same magnitude as vector C, which is also 100m. Additionally, the angle of vector C, 36.9 degrees, is the same as the angle between the +x axis and vector A, making them equal in direction as well. Therefore, vector A and vector C are equal.
 

Related to Vectors, magitude, scalar components

1. What is a vector?

A vector is a mathematical object that has both magnitude and direction. It is represented by an arrow pointing in the direction of its magnitude, and its length represents its magnitude.

2. How is the magnitude of a vector calculated?

The magnitude of a vector is calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In the case of a vector, the magnitude is equal to the square root of the sum of the squares of its components.

3. What are scalar components?

Scalar components are the individual parts of a vector that are parallel to the x and y axes. They are used to represent the magnitude and direction of a vector in a two-dimensional space.

4. How are vector components calculated?

Vector components can be calculated using trigonometric functions, specifically the cosine and sine functions. The x-component is equal to the magnitude of the vector multiplied by the cosine of the angle between the vector and the x-axis, while the y-component is equal to the magnitude of the vector multiplied by the sine of the angle.

5. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature, mass, and time, while examples of vectors include displacement, velocity, and force.

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