How do you find the resultant in terms of components, the magnitude of the resultant, and the resulant's angle above the x-axis?
When solving vectors, sometimes you are given the components and asked to
find the resultant. Then there are times when you are required to find the components when given the resultant. Let's investigate both:
Given: X = hor = 30, Y = ver = 40.
Find the resultant vector.
1. Draw a hor line from the origin pointing to the right.
2. Draw a ver line from the origin
pointing upward.
3. Draw a sloped line from the origin
which moves upward and to the right.
This is the resultant vector, and it
is located between the given components.
4. Label the x and y components with
the values given.
tanA = Y / X = 40 / 30 = 1.3333,
A = 53 deg.
R = X / cosA = 30 / cos53 = 50 =
the Resultant
R = 50 @ 53 Deg.
2nd Example:
Given: R = 50 @ 53 Deg.
Find the hor and ver components.
X = hor = RcosA = 50cos53 = 30.
Y = ver = RsinA = 50sin53 = 40.
I hope this is helpful.
To find the resultant of two vectors in terms of components, magnitude, and angle, follow these steps:
1. Determine the components of each vector: Break down each vector into its components along the x-axis and the y-axis. For example, if vector A has components (Ax, Ay) and vector B has components (Bx, By), then the resultant vector R will have components (Rx, Ry) where Rx = Ax + Bx and Ry = Ay + By.
2. Calculate the magnitude of the resultant: The magnitude of the resultant vector R can be found using the Pythagorean theorem. The magnitude, denoted as ||R||, can be calculated as follows: ||R|| = sqrt(Rx^2 + Ry^2).
3. Compute the angle above the x-axis: The angle θ can be found using the inverse tangent function (arctan) of the ratio of the y-component to the x-component of the resultant vector. The angle can be calculated as follows: θ = arctan(Ry/Rx).
By following these steps, you can find the resultant in terms of its components, its magnitude, and the angle above the x-axis.