Two Vector Problem: Calculate B_y

[Euler2718]

Homework Statement

The diagram below shows two vectors, A and B, and their angles relative to the coordinate axes as indicated.

DATA: α=45.7°; β=55.6°; |A|=3.50 cm. The vector A−B is parallel to the −x axis. Calculate the y-component of vector B.

Homework Equations

rsinθ=y

The Attempt at a Solution

A-B is parallel to x so A_{y} must equal B_{y} ? Therefore, 3.5sin45.7 = A_{y} = B_{y} = 2.50 cm ; which is wrong. I'm a bit confused here. It tells me "Since the sum vector (A−B) has no y-component, vector A must have the same y-component as vector B. As shown, 'east' is for +x, and 'north' for +y, thus the answer can be negative. " Did I mess up the calculation?

 

[andrewkirk]

A-B is parallel to x so A_{y} must equal B_{y} ? Therefore, 3.5sin45.7 = A_{y} = B_{y} = 2.50 cm ; which is wrong.

Why do you say it's wrong? They haven't given you a magnitude for B so you just need to choose a magnitude for B that, given its angle, makes its vertical component equal to 2.50.

 

[Euler2718]

Why do you say it's wrong? They haven't given you a magnitude for B so you just need to choose a magnitude for B that, given its angle, makes its vertical component equal to 2.50.

It's part of an online assignment, to which when I enter 2.50 cm it tells me it's incorrect.

 

[andrewkirk]

Perhaps they really meant to ask you the magnitude of B, because if they didn't want that they wouldn't have needed to give you the angle $\beta$. Try calculating and entering that and see if it accepts it.

If that doesn't work, the next thing I'd try is the x component of B.

 

[Euler2718]

Perhaps they really meant to ask you the magnitude of B, because if they didn't want that they wouldn't have needed to give you the angle $\beta$. Try calculating and entering that and see if it accepts it.

Sorry, I should of specified. I supposed they give you β because there's other parts to the question:

Calculate the x-component of the vector A−B.

Calculate the magnitude of the vector A+B.

I do think it's being explicit though, in wanting the y-component rather than the vector. I could try but I have four more tries left.

 

[andrewkirk]

Perhaps they want a minus sign on the 2.5. The word 'component' can refer either to an unsigned vector or to a signed scalar. If they mean the latter, the answer would be -2.50 since the vertical component is downwards and the positive y direction is up..

 

[Euler2718]

Perhaps they want a minus sign on the 2.5. The word 'component' can refer either to an unsigned vector or to a signed scalar. If they mean the latter, the answer would be -2.50 since the vertical component is downwards and the positive y direction is up..

Wow...

I still don't understand though. So is it that if the vector is 'moving downwards' in a Cartesian plane, the y-component, regardless of the quadrant it resides in, will be negative? Vice versa for 'moving upwards'?

 

[andrewkirk]

Yes that's right, although it would be more accurate to say pointing downwards rather than moving.

Vectors don't have a location. A vector is just a direction and a magnitude. In fact it's a little odd that the two vectors are drawn the way they are, rather than head-to-tail as is the usual convention. I guess that in this case they didn't want to draw them head to tail because they want you to calc things about both A - B and A + B and those two give different head to tail diagrams.

 

[Chestermiller]

The y component of A is -2.5. The y component of A - B is y_A - y_B=0. Therefore, y_B=y_A= -2.5

 

[Euler2718]

Having trouble with "Calculate the magnitude of the vector A+B. " My friends and I are stuck and what seems like a easy problem.

 

[Chestermiller]

Having trouble with "Calculate the magnitude of the vector A+B. " My friends and I are stuck and what seems like a easy problem.

What are the x- and y components of the vectors A and B?

 

[Euler2718]

What are the x- and y components of the vectors A and B?

A_{y} = 2.5
B_{y} = -2.5
A_{x} = 2.44
B_{x} = 3.65 (-3.65? it shouldn't matter since Pythagoras)

We did:

$$\sqrt{(2.44+3.65)^{2} + (2.5+2.5)^{2} } = 7.88 cm$$

Which it tells me is wrong.

 

[Euler2718]

Would A+B be parallel to the y-axis?

 

[Chestermiller]

Would A+B be parallel to the y-axis?

No. In the figure, is the x component of A positive or negative? In the figure, is the x component of B positive or negative?

Chet

 

[Euler2718]

No. In the figure, is the x component of A positive or negative? In the figure, is the x component of B positive or negative?

Chet

I got it now, thanks. Answer was 5.14 cm