Three vectors are shown in the figure. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) magnitude and (b) the angle within the positive x axis.
A is in quadrant one with a length of 44.0 and an angle of 28.
B is in quadrant two with a length of 26.5 and an angle of 56.
C is on the y axis facing down with a length of 31.0
Three vectors are shown in the figure. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) magnitude and (b) the angle within the positive x axis.
no figure.
To determine the sum of the three vectors, you need to add the individual components of each vector.
Let's denote the three vectors as A, B, and C.
Step 1: Find the components of each vector.
Look at the figure and determine the x and y components of each vector. The x component is the projection of the vector onto the x-axis, and the y component is the projection of the vector onto the y-axis.
For example, let's assume that the x and y components of vector A are Ax and Ay, respectively. Similarly, let the x and y components of vector B be Bx and By, and for vector C, let the components be Cx and Cy.
Step 2: Add the x and y components separately.
Add the x components of the three vectors:
Rx = Ax + Bx + Cx
Add the y components of the three vectors:
Ry = Ay + By + Cy
Step 3: Calculate the magnitude of the resultant vector.
To find the magnitude (R) of the resultant vector, use the Pythagorean theorem:
R = sqrt(Rx^2 + Ry^2)
Step 4: Calculate the angle within the positive x-axis.
To find the angle (θ) within the positive x-axis, use trigonometry:
θ = arctan(Ry / Rx)
By following these steps, you can determine the sum of the three vectors in terms of magnitude and angle with the positive x-axis.
It wont let me insert the figure into the text box.
changing each vector to x,y components:
I assume each angle is measured from the x axis, if not, you did not specify, you have to modify this:
A=44cos28 xbar + 44sin28 ybar
B=26.5cos(180-56)+26.5sin(180-56)ybar
C= 0 xbar-31 ybar.
Sum xbars= sum of those above; sum ybars= sum of those ybars above.
Resultant= sqrt(sumxbar^2 + sumybar^2)
angle= arctan(sumybar/sumxbar).
In vectors, in the future, please note how the angles are measured. It is very standard to measure the angles from y axis (or OOO N), clockwise.