What are the Components of a Vector Given its Magnitude and Direction?

[sp33dk1lls]

Homework Statement

Two force vectors are shown in the figure (not drawn to scale), and the total force vector C is the sum of A and B:C=A+B. If the magnitude of the total force is C = 80 N and its direction is specified by the angle measured from +x axis to be θC = −110˚, find B and φ for the force vector B.

Homework Equations

C_x= A_x+ B_x
C_y= A_y+ B_y
C= sqrt(C_x^2+C_y^2)?
tanθ_c=C_y/C_x?

The Attempt at a Solution

A_x=-150cos30=-130
A_y=150sin30=75
C_x=80sin(-110)=-75.2
C_y=80cos(-110)=27.4

C_x= A_x+ B_x
-75.2= -130 + B > B= 54.8
27.4= 75 + B > B=-47.6

Not sure if I'm doing this right.

 

[Doc Al]

C_x=80sin(-110)=-75.2
C_y=80cos(-110)=27.4

You mixed up the components here. And be careful with signs.

 

[sp33dk1lls]

ok i got that. now i could use a little hint about what to do next. I'm sure how to get the single magnitude for B.

 

[woodyallen1]

Both components of B sould be positive. Try make a drawing and work with reduced angles. 110 is at the second quarter, so work with 30 at the second quarter.

 

[woodyallen1]

i meant third quarter

 

[woodyallen1]

the components of A and C are Ax=-75sqrt2 Ay=75. Cx=-40 and Cy=-40sqrt2

 

[woodyallen1]

Bx=-40-75sqrt2 By=75-40sqrt2 and tanθB= By/Bx and it is at the second quarter. to find the angle subtract from 180, θB.

 

[sp33dk1lls]

what was your final answer by doing your method because it seems different from mine. i got B=182 N and the angle 34.3

 

[woodyallen1]

Bx=102 and By=-112. Do we agree so far?

 

[sp33dk1lls]

the way you did it yes. the way i was doing it no.

 

[Doc Al]

now i could use a little hint about what to do next. I'm sure how to get the single magnitude for B.

Just set up the equations for components:

Ax + Bx = Cx
Ay + By = Cy

And solve for Bx and By. Using the components, you can compute the magnitude.