Calculating New Vector Components

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In summary, vectors are mathematical quantities that have both magnitude and direction. They are widely used in various scientific fields and can represent physical quantities such as force, velocity, and acceleration. Some examples of vector quantities include displacement, velocity, and force. Vectors can be added and subtracted using specific mathematical operations. The main difference between a vector and a scalar is that a vector has both magnitude and direction, while a scalar only has magnitude and can be represented by a single number.
  • #1
josh84
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Homework Statement


A certain vector in the xy plane has an x component of 4 and a y component of 10. It is rotated in the xy plane so its x component is doubled. Its new y component is about:
A. 20
B.7.2
C.5.0
D.4.5
E.2.2

Homework Equations





The Attempt at a Solution

 
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  • #2
You must show some work. What do you know about vectors? Do you know how to find the magnitude?
 
  • #3


The new x component would be 8, since it is doubled from the original value of 4. To find the new y component, we can use the Pythagorean theorem to calculate the magnitude of the vector. The original magnitude can be found using the formula sqrt(x^2 + y^2), which in this case would be sqrt(4^2 + 10^2) = sqrt(116) = 10.77. Since the x component has doubled, the new magnitude would also double, making it equal to 21.54. To find the new y component, we can use the formula y = sqrt(new magnitude^2 - x^2), which in this case would be sqrt(21.54^2 - 8^2) = sqrt(462.72 - 64) = sqrt(398.72) = 19.96. Therefore, the new y component is approximately 19.96. Option A, 20, is the closest answer.
 

1. What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. It is represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude of the vector.

2. How are vectors used in science?

Vectors are used in many scientific fields, such as physics, engineering, and biology. They are used to represent physical quantities such as force, velocity, and acceleration, and they are also used in mathematical models to describe and predict various phenomena.

3. What are some examples of vector quantities?

Some examples of vector quantities are displacement, velocity, acceleration, force, and momentum. These quantities have both magnitude and direction, and can be represented by vectors.

4. How are vectors added and subtracted?

Vectors are added and subtracted using mathematical operations called vector addition and vector subtraction. In vector addition, the components of two or more vectors are added together to find the resultant vector. In vector subtraction, the components of one vector are subtracted from the components of another vector to find the resultant vector.

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

A vector has both magnitude and direction, while a scalar only has magnitude. Scalars can be represented by a single number, while vectors require at least two numbers (or components) to be fully described. Examples of scalars include temperature, time, and mass, while examples of vectors include displacement, velocity, and force.

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