Use components to find Direction of the resultant of the three pulls?

1. Sep 22, 2011

valeriex0x

Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in the figure. (985N @ 31 Degrees Quad 1, 788 N 32 degrees Quad 2, and 411N 53 degrees quad 3.

How do I find the direction of the resultant of the three pulls? Enter your answer as the angle counted from +x axis counterclockwise direction.

I have already found the three x components of the three pulls. I have already found the y components of each of the three pulls. And I have already found the magnitude of the resultant of the three pulls. All of my answers to those parts are correct. I just dont understand what I am supposed to do to find the direction of the resultant of the three pulls. Please help!

2. Sep 22, 2011

grzz

3. Sep 22, 2011

valeriex0x

V1 points north east, V2 points north west, and V3 points Southwest. Angle theta (31, 32, 53) is between the vector and the x axis. carteesion plane

4. Sep 22, 2011

valeriex0x

y components:
985N sin(31)= 507
788N cos(32)= 668
411N sin(53)=-328

x components:
985N cos(31)= 844
788N sin(32)= -417
411N cos(53)= -247

tan^-1 (507/844)= 30.98
tan^-1 (668/-417)= -58.02
tan^-1 (-328/-247)= 53.01

5. Sep 22, 2011

valeriex0x

Sum Fx= 179.4
Sum Fy= 847

total Fsum: rad (179)^2 + (847)^2 = 865 magnitude of the resultant of the three pulls

6. Sep 22, 2011

grzz

Suppose the resultant R is in the 4th quad i.e. NW. Then the angle A between the resultant R and the resultant of all x-components, X, is given by cosA = X/R.

7. Sep 22, 2011

valeriex0x

So are you saying I should use cos^-1 (x/865)? I'm not sure i'm following what x would be! :/

8. Sep 22, 2011

grzz

If the angle 32 degrees is betweem 788N and the negative x-axis, then the y-comp is given by 788sin32 and not by 788cos32.

9. Sep 22, 2011

valeriex0x

wait! cos^-1 (179/865) = 77.77????????????? degreees!???

10. Sep 22, 2011

valeriex0x

yayy! the answer was 77 degrees. Thanks for the guidance. regarding the sin cos stuff with the components all those answers were correct so i might have explained the quads incorrectly. thanks for urrrrr help!

11. Sep 22, 2011

grzz

I said X , the resultant of all x-components of the three given forces.