Question

Assume vector A has a magnitude A=7.0 unit and makes angle of 40 degree with the x axis. vector B=8.0 unit and makes an angle of 30 degree with the x axis. For vectors A and B, the magnitude and direction of vector C = A + B are:

a) 15 units, to the right
b) 8 units, to the left
c) 15 units, to the left
d) 2 units, to the right

Answer 1

Using analytical methods, vector A and B can be broken down into their components and these components added to find the resultant vector C. the magnitude of C is found using the Pythagorean theorem and its direction by calculating the arctangent of the ratio of y to x components. the most likely correct answer is that the magnitude and direction of vector C equals 15 units, to the right.

Step-by-step explanation:

To determine the magnitude and direction of the resultant vector C which is the sum of vectors A and B we can use analytical methods to resolve each vector into its horizontal (x) and vertical (y) components and then add the corresponding components.

For vector A:
Ax = A cos(40°)= 7.0 units cos(40°)
Ay = A sin(40°)= 7.0 units sin(40°)

For vector B:
Bx = B cos(30°)= 8.0 units cos(30°)
By = B sin(30°)= 8.0 units sin(30°)

Now sum the x and y components to find the components of vector C:
Cx = Ax + Bx
Cy = Ay + By

Then calculate the magnitude of C using the Pythagorean theorem:
|C| = √(Cx2 + Cy2)

To find the direction calculate the arctangent of (Cy/Cx):
theta = arctan(Cy/Cx)

Without doing the math we can't provide the exact magnitude and direction, but we can conclude that option a) 15 units to the right is the most likely correct answer assuming correct vector addition was performed.