# What are (a) the magnitude and (b) the angle

1. Homework Statement [/b]

In the sum A-> + B-> = C->, A-> vector has a magnitude of 13.8 m and is angled 44.0° counterclockwise from the +x direction, and vector C-> has a magnitude of 16.8 m and is angled 18.8° counterclockwise from the -x direction. What are (a) the magnitude and (b) the angle (relative to +x) of B->? State your angle as a positive number.

2. Homework Equations [/b]

3. The Attempt at a Solution

I dont know if its right or not. :(

sin(44)13.8 = 9.58628 for A
sin(18.8)16.8 = 5.41406368 for C
cos(44)13.8=9.926889245 for A
cos(18.8)16.8=15.90370757 for C
that's the two components of A and C. since you're trying to find B
it's C - A = B.
in the x direction: 5.41406368 - 9.58628 = -4.172
in the y direction: 15.90370757 - 9.926889245 = 5.976

The magnitude is simply sqrt (x component^2 + y component^2) = 7.288

the angle relative to +x is tan^-1(x component/y component) = tan^-1(-4.172/5.976) = -34.9 degrees.

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berkeman
Mentor

1. Homework Statement [/b]

In the sum A-> + B-> = C->, A-> vector has a magnitude of 13.8 m and is angled 44.0° counterclockwise from the +x direction, and vector C-> has a magnitude of 16.8 m and is angled 18.8° counterclockwise from the -x direction. What are (a) the magnitude and (b) the angle (relative to +x) of B->? State your angle as a positive number.

2. Homework Equations [/b]

3. The Attempt at a Solution

I dont know if its right or not. :(

sin(44)13.8 = 9.58628 for A
sin(18.8)16.8 = 5.41406368 for C
cos(44)13.8=9.926889245 for A
cos(18.8)16.8=15.90370757 for C
that's the two components of A and C. since you're trying to find B
it's C - A = B.
in the x direction: 5.41406368 - 9.58628 = -4.172
in the y direction: 15.90370757 - 9.926889245 = 5.976

The magnitude is simply sqrt (x component^2 + y component^2) = 7.288

the angle relative to +x is tan^-1(x component/y component) = tan^-1(-4.172/5.976) = -34.9 degrees.
You are using the right methods, but I think you may have a sign wrong in one of the calculations (I could be wrong, though).

Look at where the vector C is pointing. You are given its angle of rotation from the negative x axis, not the positive one. So the x component of the C vector will be negative.

It would help clarity if you could show your answers for the two vectors A and C like this:

A = (Ax, Ay)
C = (Cx, Cy)

where you put in your numbers (with correct signs) into the parenthesis. That will help you to keep your signs right when you calculate the difference vector B. It will also help you if you sketch the vectors on paper to check that the signs and magnitudes are working out correctly.

um i don't get what your saying