Answer:
1. The horizontal component is 37.74 N due to east
The vertical component is 16.02 N due to north
2. The magnitude of the resultant vector is 11.6338 m
Explanation:
The resultant vector is the vector sum of two or more vectors
It has magnitude and direction
Its magnitude = [tex]\sqrt{x^{2}+y^{2}}[/tex], where x is its component
in the direction of x-axis and y is its component in the direction of y-axis
Its direction = [tex]tan^{-1}\frac{y}{x}[/tex] with respect to x-axis
So the components of the resultant vector of magnitude R and direction
Ф with the positive part of x-axis are:
Horizontal component = R cosФ
Vertical component = R sinФ
1.
Slanted vector has a magnitude of 41 N and is at an angle of 23°
north of east
We need to find the horizontal and vertical components with their
directions
North of east means 23° between east and the ray of the vector
If we consider that east is the positive part of the x-axis
Then R = 41 N and Ф = 23°
The horizontal component = (41) cos(23) = 37.74 N due to east
The vertical component = (41) sin(23) = 16.02 N due to north
The horizontal component is 37.74 N due to east
The vertical component is 16.02 N due to north
2.
A horizontal component vector has a magnitude of 11 m
If the resultant vector forms an angle with this component of 19°
The horizontal component = R cosФ
11 = R cos(19)
Divide both sides by cos(19)
11.63 = R
The magnitude of the resultant vector is 11.6338 m
