Vector addition - Finding V2 when V1 and V1+V2 are given

[exi]

Homework Statement

Particle has two displacements.

1 - 11m, 89 degrees
2 - ?
1+2 - 8.6m, 129 degrees

So:
1 = (11, 89°)
2 = ?
1+2 = (8.6, 129°)

Homework Equations

X-component = M x cos(Θ)
Y-component = M x sin(Θ)

Total magnitude = sqrt((total x-component)² + (total y-component)²)

Total angle = tan-1 (total y-component / total x-component)

The Attempt at a Solution

I'm not terribly sure how I should best try to find the magnitude and angle of the second portion of the movement here. I would've tried to solve for total magnitude, but I'm missing both X and Y components for #2, so... what should I do?

 

[Doc Al]

Of course you're missing those components--you have to solve for them! Set up an equation for x-components; from this you can solve for the unknown x-component of vector #2. Then do the same for the y-components.

 

[Chi Meson]

Think this way:
1 + 2 = R

2 = R - 1

2 = R + (-1)

 

[exi]

Of course you're missing those components--you have to solve for them! Set up an equation for x-components; from this you can solve for the unknown x-component of vector #2. Then do the same for the y-components.

That's the thing. I'm probably making this far more complicated than it has to be, but the first idea or three that come to mind on how to do exactly that involve information that I don't have, like angles for #2.

I'd appreciate a kick-start on this one.

 

[Doc Al]

I'll call your vectors A and B (instead of 1 and 2). So you have:
A + B = R

You are given A and R; you need to find B. So solve for the components. Set up two equations:

(1) Ax + Bx = Rx
You should be able to compute and plug in the x-components of A and R. Then you can solve for Bx.

As Chi Meson explained:
Bx = Rx - Ax

(2) Ay + By = Ry
Same thing, only now you are doing the y-components.

So find Bx and By, then you can find the magnitude and direction of B.

 

[esalihm]

perhaps setting up a table with assigning +x, -x, +y and -y to appropriate components would help you.
rest is just mathematical subtraction

 

[exi]

I'll call your vectors A and B (instead of 1 and 2). So you have:
A + B = R

You are given A and R; you need to find B. So solve for the components. Set up two equations:

(1) Ax + Bx = Rx
You should be able to compute and plug in the x-components of A and R. Then you can solve for Bx.

As Chi Meson explained:
Bx = Rx - Ax

(2) Ay + By = Ry
Same thing, only now you are doing the y-components.

So find Bx and By, then you can find the magnitude and direction of B.

Yep, I was definitely making this far more complicated than it was. For whatever reason, I kept thinking that it couldn't possibly be as easy as determining the component vectors of R and working out B from that.

Obviously, it is.

Thanks for the slap back into rational thinking