The vectors that are shown in the figure below. The magnitudes are F1 = 1.81f, F2 = f, and F3 = 2.00f, where f is a constant. Description of the figure--On the first quadrant the angle is 60 degree with F3 as the hypotenuse and on the second quadrant the angle is 30 degree with F2 as the hypotenuse. (a) Use the coordinate system shown in the figure above to find

Question

The vectors that are shown in the figure below. The magnitudes are F1 = 1.81f, F2 = f, and F3 = 2.00f, where f is a constant. Description of the figure--On the first quadrant the angle is 60 degree with F3 as the hypotenuse and on the second quadrant the angle is 30 degree with F2 as the hypotenuse. (a) Use the coordinate system shown in the figure above to find

R = F1 + F2 + F3 in component form in terms of f. (b) If Rx = 0.25,what is Ry?

Answer 1

I cannot follow the description, expecially how the angles are measured.

Here is a sure fire way to solve these.
a) measure all angles from +x, counter clockwise.
b) then break each vector up into the following components:
fx= F cosTheta
fy= F sinTheta
keeping theta measured from x+

c) then add the vectors Rx=(fx1+fx2+fx3) and the same for Ry.

Note that because of the periodicity of sine, cosine functions, you have to make certain the final angle is in the right triangle, as your calculator may only give the principal angles

Answer 2

1st: Part a):To find R, first find f1x,f1y,f2x; f2y, f3x, f3y.

2nd: f1x is 0i because it is at the origin,f1y is-1.81j because that was giving as the arrow point toward the negative direction. For f2x, f was giving as 1f take it and multiply with cos(30) --> 1*cos(30)= -.866i because x in the second quadrant is negative; f2y do the same thing again with sin(30) this time-->1*sin(30)=.500j. For f3x, f was giving as 2.00f take it and multiply with cos(60)-->2*cos(60)= 1.00i; f3y do the same thing but with sin (60) this time-->2*sin(60)=1.73j. 3rd: To find R, add all the fx together on one side and fy together on the other side.-->R=(0i+-.866i+1.00i)+(-1.81j+.500j+1.73j)
4th: answer for R-->R=.134i+.420j
5th: Part b):To find Ry, we know Rx=.25i take it and divide with .134i, the value that was find in R--> .134i/.25i=.536
6th: to get the answer for Ry,take .420j, the value that was find in R and divide by.536--> .420j/.536= .784j as answer.

Answer 3

To solve the problem, we can break down each vector into its x and y components using trigonometry.

(a) We'll start by finding the x and y components of each vector.

For F1:
The angle in the first quadrant is 60 degrees, and F3 is the hypotenuse.
The x-component of F1 is given by F1x = F1 * cos(60°) = 1.81f * cos(60°) = 0.9055f
The y-component of F1 is given by F1y = F1 * sin(60°) = 1.81f * sin(60°) = 1.5682f

For F2:
The angle in the second quadrant is 30 degrees, and F2 is the hypotenuse.
The x-component of F2 is given by F2x = F2 * cos(150°) = f * cos(150°) = -0.866f
The y-component of F2 is given by F2y = F2 * sin(150°) = f * sin(150°) = 0.5f

For F3:
The angle in the first quadrant is 60 degrees, and F3 is the hypotenuse.
The x-component of F3 is given by F3x = F3 * cos(60°) = 2.00f * cos(60°) = f
The y-component of F3 is given by F3y = F3 * sin(60°) = 2.00f * sin(60°) = 1.732f

Now, we can add up all the x and y components to find R in component form:
Rx = F1x + F2x + F3x = 0.9055f + (-0.866f) + f = 1.0395f
Ry = F1y + F2y + F3y = 1.5682f + 0.5f + 1.732f = 3.8002f

So, R = Rx î + Ry ĵ = 1.0395f î + 3.8002f ĵ

(b) If Rx = 0.25, we can set the x component equation equal to 0.25 and solve for f:
0.25 = 1.0395f
f = 0.2402

Now that we have the value of f, we can substitute it into the equation for Ry:
Ry = 3.8002f = 3.8002 * 0.2402 = 0.9131

Therefore, Ry = 0.9131.