Vector A=125 m/s, 40 degrees north of west. Vector B is 185 m/s, 30 degrees south of west and vector C is 175 m/s 50 east of south. How do you find A+B-C by vector resolution method?
The resultant vector will be
First, you will resolve each vector (given here in standard form) into rectangular components (
Then, you will add together the
Finally, convert the resultant into standard form.
Resolve into rectangular components
Note that all given angles have been changed to standard angles (counterclockwise rotation from the
Now, add the one-dimensional components
#R_y = A_y+B_y-C_y = 80.35-92.50+112.49=100.34m/s
This is the resultant velocity in rectangular form. With a negative
Now, convert to standard form:
This angle looks a bit strange! Remember, the vector was stated to point into the second quadrant. Our calculator has lost track of this when we used the
To find this angle, add 180° to the (incorrect) result above. The angle we want is 165.6°.
If you get into the habit of always drawing a reasonably accurate diagram to go along with your vector addition, you will always catch this problem when it occurs.