As a reference, please look at the attached image. From the magnitude and direction of the vector we can compute its horizontal and vertical components as:
[tex]V_x = - V \cdot cos(23.4 \º) = -22.76[/tex]
[tex]V_y =V \cdot sin(23.4 \º) = 9.85[/tex]
Further explanation
A vector, in the wider sense of knowledge, is a mathematical tool which shapes itself according to the user's insight. This means that vectors can represent many things... In physics, for example, we imagine vectors as pointy arrows which have a size and a direction.
Having the size and the direction, it is easy to compute the components of a vector with respect of a reference frame. The computation is very simple because, as it is seen in the attached image, we can compute the x and y component of the vector with trigonometry. By using the right triangle with angle 23.4º, we get that:
[tex]V_x = - V \cdot cos(23.4 \º) = -22.76[/tex]
[tex]V_y =V \cdot sin(23.4 \º) = 9.85[/tex]
Having these 2, it is easy to obtain the magnitude of vector V and its direction. The magnitude will be given by pythagoras theorem since:
[tex]|V|= \sqrt{(V_x)^2+(V_y)^2} = \sqrt{(-22.76)^2+(9.85)^2} = 24.8[/tex]
And it's direction will be given by:
[tex]\theta = \tan^{-1} \left (\frac{V_y}{V_x} \right )= \tan^{-1} \left (\frac{9.85}{-22.76} \right ) =2.733[/tex] radians
Which represents an angle of 156.6º with respect to the positive side of the x axis (so 23.4º with the negative side of the x axis).
Learn more
- Sum of 2 vectors: https://brainly.com/question/2927458
- Other problems of vectors: https://brainly.com/question/4579006
Keywords
Vectors, angles, horizontal component, vertical component
