Finding magnitude of vector B given resultant and angle

[Ampere]

Homework Statement

The resultant of vectors A and B has a magnitude of 20 units. A has a magnitude of 8 units, and the angle between A and B is 40 degrees. Calculate the magnitude of B.

Homework Equations

Trig, resolving vector components.

The Attempt at a Solution

I worked out the equations and got |B| = 13.20 units. But, this isn't any of my choices. Am I right, or am I missing something here?

 

[ehild]

Your result is correct.

ehild

 

[Dick]

Homework Statement

The resultant of vectors A and B has a magnitude of 20 units. A has a magnitude of 8 units, and the angle between A and B is 40 degrees. Calculate the magnitude of B.

Homework Equations

Trig, resolving vector components.

The Attempt at a Solution

I worked out the equations and got |B| = 13.20 units. But, this isn't any of my choices. Am I right, or am I missing something here?

That's what I got. But maybe we made the same mistake? Mind showing you you got that?

 

[Ampere]

Sure. Align A along the +x axis, with B at 40 degrees above that.

Then:

Ax = 8
Ay = 0
Bx = Bcos(40)
By = Bsin(40)

So Rx = 8+Bcos(40)
Ry = Bsin(40)

The magnitude of the resultant R would be sqrt(Rx^2 + Ry^2), which is equal to 20, so

20 = sqrt((8+Bcos(40))^2 + (Bsin(40))^2). Solving for B yields 13.20.

For the record, my choices were

12.6
16.2
14.8
18.4

But I don't see how you could get any of them.

 

[Dick]

Sure. Align A along the +x axis, with B at 40 degrees above that.

Then:

Ax = 8
Ay = 0
Bx = Bcos(40)
By = Bsin(40)

So Rx = 8+Bcos(40)
Ry = Bsin(40)

The magnitude of the resultant R would be sqrt(Rx^2 + Ry^2), which is equal to 20, so

20 = sqrt((8+Bcos(40))^2 + (Bsin(40))^2). Solving for B yields 13.20.

For the record, my choices were

12.6
16.2
14.8
18.4

But I don't see how you could get any of them.

Same thing I did. If ehild got the same result as us I have little doubt that it's correct. Probably just a mistake in the choices.

 

[Ampere]

Awesome, thanks.

 

[ehild]

Same thing I did. If ehild got the same result as us I have little doubt that it's correct. Probably just a mistake in the choices.

I used Cosine Law, with 140°angle between vectors A and B, and got the same result.

ehild

 

[ehild]

Same thing I did. If ehild got the same result as us I have little doubt that it's correct. Probably just a mistake in the choices.

I used Cosine Law, and got the same result.

ehild