Finding vector B components from A

[jwxie]

Homework Statement

Please look at the first attachment, I need to solve question #15

Homework Equations

See the second attachment

The Attempt at a Solution

Well I got Ax = -75cm, Ay = 129.9cm but I just can't solve the problem because I got stuck at solving for Bx and By.

Attachment 3 is my work.

Please teach me how to solve the answer
by the way, the answer is 196cm at 14.7 degree below x-axis

also, if possible, may sketch the picture of this problem for me, please?

 

[LowlyPion]

Homework Statement

Please look at the first attachment, I need to solve question #15

Homework Equations

See the second attachment

The Attempt at a Solution

Well I got Ax = -75cm, Ay = 129.9cm but I just can't solve the problem because I got stuck at solving for Bx and By.

Please teach me how to solve the answer
by the way, the answer is 196cm at 14.7 degree below x-axis

also, if possible, may sketch the picture of this problem for me, please?

What you want to do is exploit the vector addition of the components.

In this problem they have given you the initial displacement vector and the final result.

Split the 3 vectors into their x,y components. And then write the equations for x adding to the result and then y adding to the result.

Sure Vector 2 components will be unknown but you will have two equations and each equation will give you each component of Vector 2. Then solve and do the tan^-1 as you did in your first try.

 

[jwxie]

hello lowly, thank you for your quick reply
but i am really having problem with this
so i did... (not quite sure everything you mean), but

Ax = ACos = -75cm
Ay = ASin = 129.9 cm

Bx = BCos
By = BSin

Rx = Ax+Bx --> Rx = -75cm+Bx
Ry = Ay+By --> Ry = 129.9cm+By

R = 140 (resultant), and since R^2 = Rx^2+Ry^2, then i have
140^2 = (-75cm+Bx)^2 + (129.9cm+By)^2
but doesn't it turn into unknown solution? i can't solve for either component...

 

[jwxie]

i have tried this really hard...=.= still can't answer it
it sounds stupid but.. i don't know why i got stuck

 

[jwxie]

anyone would like to give a hand?
quote:
And then write the equations for x adding to the result and then y adding to the result.

what do you mean?

 

[jwxie]

i actually figured it out (not yet to the right answer)
but here is what i thought

since R = sqrt of x^2 + y^2
then the x = the sum of ax+bx
and y = sum of ay+ay

now the problem is, after many trial out, the closest i can get is 189.7

i just need to confirm 2 things

1) to find Vector A(1)'s component, is the angle 120, or 60?
2) to find the R vector component, we use 35, -35, or 145 degree?

 

[alphachapmtl]

A = (Ax,Ay) = (150 cos120, 150 sin120) = (-150 sin30, 150 cos30) = (-75, 75*sqrt(3))
R = (Rx,Ry) = (140 cos35, 140 sin35) = ()
A+B=R so B=R-A
B = (Rx-Ax, Ry-Ay) = (140 cos35 + 75 , 140 sin35 - 75*sqrt(3))
cos(35) = 0.819152044
sin(35) = 0.573576436
75 * sqrt(3) = 129.903811
B = (Rx-Ax, Ry-Ay) = (114.681286 + 75 , 80.3007011 - 129.903811) = (189.681286, -49.6031095)

 

[jwxie]

ty all
i figured out my calculation was wrong in the first place, so i didn't get a correct solution
thank you very much