Three vectors are shown in Fig. 3-32 (A = 60.0 , B = 56.0°). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors.
(a) Give the resultant in terms of components.
(b) What is the magnitude of the resultant?
What is the resultant's angle above the +x axis?
What three vectors, you only listed two, and then only the angles.
46.8
That is absolutely meaningless.
To determine the sum of the three vectors and find the resultant, we need to break down each vector into its horizontal and vertical components. Let's go step by step:
(a) Finding the Resultant in terms of Components:
1. Start by writing down the given magnitudes and angles for each vector:
Vector A: Magnitude = 60.0, Angle = 0° (along the x-axis)
Vector B: Magnitude = 56.0, Angle = 56.0° above the x-axis
Vector C: Magnitude = Unknown, Angle = Unknown
2. Convert the angles to their respective component form:
For Vector B, we need to find its horizontal and vertical components. The horizontal component (Bx) can be found using cosine, and the vertical component (By) can be found using sine:
Bx = B * cos(angle) = 56.0 * cos(56.0°)
By = B * sin(angle) = 56.0 * sin(56.0°)
3. Determine the resultant components by adding the individual components:
Rx = Ax + Bx + Cx
Ry = Ay + By + Cy
4. Keep in mind that Vector A is along the x-axis, so its components are:
Ax = 60.0, Ay = 0
5. Since the magnitudes and angles for Vector C are not given, we cannot determine its components (Cx and Cy) at this point. So, we represent them as unknown (Cx = ? and Cy = ?).
(b) Finding the Magnitude of the Resultant:
To find the magnitude of the resultant (R), we can use the Pythagorean theorem:
R = sqrt(Rx^2 + Ry^2)
(c) Finding the Resultant's Angle Above the +x Axis:
To find the angle above the +x axis of the resultant vector, we can use the inverse tangent (arctan) function:
θ = arctan(Ry / Rx)
By following these steps, you should be able to determine the sum of the three vectors, find the magnitude of the resultant, and calculate the resultant's angle above the +x axis.