Respuesta :
Using vector concepts, it is found that:
- 1. The vertical component is 9.
- 2. The horizontal component is 13.
- 3. The magnitude is of [tex]\mathbf{\sqrt{65}}[/tex] units.
- 4. The horizontal component is 9.2345 newtons.
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- A vector has the format (x,y), in which x is the horizontal component and y is the vertical component.
- The components of a vector are given by the subtraction of the endpoint by the start point.
- The magnitude of a vector (x,y) is given by [tex]\sqrt{x^2 + y^2}[/tex]
- In function of the magnitude M and an angle [tex]\alpha[/tex], the coordinates can be given by: [tex](x,y) = (x\cos{\alpha}, y\cos{\alpha})[/tex]
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Item 1:
- Starts at point (8, -1) and ends at (5,8).
- The vertical component is the subtraction of the y-coordinates, thus: [tex]8 - (-1) = 8 + 1 = 9[/tex]
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Item 2:
- Starts at point (-5, 8) and ends at (8,-9).
- The horizontal component is the subtraction of the x-coordinates, thus: [tex]8 - (-5) = 8 + 5 = 13[/tex]
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Item 3:
- Starts at point (-9, -4) and ends at (-1,-5).
- The coordinates are: [tex](-1 - (-9), -5 - (-4)) = (-1 + 9, -5 + 4) = (8, -1)[/tex]
- The magnitude is: [tex]\sqrt{8^2 + (-1)^2} = \sqrt{64 + 1} = \sqrt{65}[/tex]
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Item 4:
- Magnitude of 27, angle of 70 degrees, thus:
- [tex]x = 27\cos{70} = 9.2345[/tex]
- The horizontal component is 9.2345 newtons.
A similar problem is given at https://brainly.com/question/19725792
A vector can be represented by a line on the coordinate plane such that the length of the line and the direction of the line gives the magnitude and direction of the vector
The components and magnitudes of the vectors are;
1. The vertical component of the vector is 9
2. The horizontal component of a vector is 13
3. The magnitude of the vector is 3
4. The horizontal component of the pulling force is approximately 9.23 N
The reason the above values are correct are as follows:
The given coordinates of the vectors are as follows;
1. Starting point coordinate: (8, -1), ending point coordinate (5, 8)
Required:
The vertical component of the vector
Solution:
The vertical component of the vector is given by the difference of the y-coordinates (-1, and 8) as follows;
Vertical component = 8 - (-1) = 9
The vertical component of the vector = 9
2. The known parameter:
The starting point coordinate is (-5, 8), and the ending point coordinate is (8, -9)
Required:
The horizontal component of the vector
Solution:
The horizontal component of a vector is given by the difference of the x-coordinate values (-5 and 8), taking into consideration of the direction of the vector, as follows;
The horizontal component of a vector = 8 - (-5) = 13
3. Known parameter
Starting point coordinate of the vector (-9, -4), the ending point coordinate of the vector (-1, -5)
Required:
The magnitude of the vector
Solution:
The magnitude of the vector is given by the length of the line on the x, y-coordinate plane as follows;
[tex]Magnitude = Length \ of \ representative \ line \ l \ = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Therefore, we have;
Magnitude of the vector = √((-5 - (-4))² + (-1 - (-9))) = 3
The magnitude of the vector = 3
4. The known parameters are;
The pulling force by Jason = 27 N
The angle which his arm makes with the horizontal = 70°
Required:
The horizontal component of the pulling force
Solution:
The component of a vector is given by the projection of the vector unto the axis being referenced
The horizontal component of the vector is given by the component in the x-axis direction
∴ The horizontal component of the vector = 27 × cos(70°) ≈ 9.23 N
Learn more about vectors here:
https://brainly.com/question/15894248
