Need help with components of vectors

[godawgs]

Homework Statement

1. Given the following force vectors: A is 27 lb at an angle of 27° clockwise from the +x-axis, and B is 44 lb at an angle of 45° clockwise from the +y-axis.

(a) Make a sketch and visually estimate the magnitude and angle of the vector C such that 2A+ C − B results in a vector with a magnitude of 37 lb pointing in the +x direction. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Repeat the calculation in Part (a) using the method of components and compare your result to the estimate in (a).
C=_______ lb
magnitude _______ lb
direction_______° counterclockwise from the +x-axis

Homework Equations

The Attempt at a Solution

Comp Ax 27cos(27) --> 24.1
Comp Ay 27sin(27) --> 12.3

Comp Ay 44cos(45) --> 31.1
Comp By 44sin(45) --> 31.1

Cx = Ax + Bx == 24.1 + 31.1 = 55.2
Cy = Ay + By == 12.3 + 31.1 = 43.4

C^2 = A^2 + B^2 == 55.2^2 + 43.4^2 == 4930.6
C = sqrt(4930.6) == 70.21 lbs

I attempted to add the components of the two vectors and then use the pythagorean theorem to find the magnitude of C but I feel like I'm missing a step. I think adding 3 different vectors is throwing me off... Can anyone help or walk me through the steps of the problem?

 

[fenderchik]

Hey! We're probably in the same class. I think you may have mistaken the degrees for your B vector. Since it is 56 degrees clockwise from the +y axis, it is actually 270 degrees + 56 degrees. Thus your components should be 44cos(315). Give that a try. Good luck!

 

[zgozvrm]

I'm not sure where fenderchik got 56[itex]^\circ[/tex] for vector B. Your problem states 45[itex]^\circ[/tex] from the positive y-axis (which lies at 90[itex]^\circ[/tex]).

Assuming your numbers are correct, you mis-judged the actual angle of vector A.
The positive x-axis lies at 0[itex]^\circ[/tex], so 27[itex]^\circ[/tex] clockwise from that is -27[itex]^\circ[/tex], or 333[itex]^\circ[/tex] (not +27[itex]^\circ[/tex]).

Otherwise, your work looks good.