In the vector sum A + B = C , vector A has a magnitude of 13.1 m and is angled 49° counterclockwise from the +x direction, and vector C has a magnitude of 15.0 m and is angled 20.0° counterclockwise from the -x direction. What are
(a) the magnitude and
(b) the direction (relative to +x of vector B?
[[[Warning! Make a graphical solution first so you will know what quadrant B lies in.]]]
magnitude = ______ m
direction = ______ degrees
I will be happy to check your answers, or critique your thinking. We don't do tests for students.
it's not a test. just a hw assignment one of a bunch of questions im stuck on.
~lor
No problem, I can help you with your assignment. Let's start by breaking down the information given to solve for vector B.
We are given:
- The magnitude of vector A, |A| = 13.1 m, and its angle counterclockwise from the +x direction, which is 49°.
- The magnitude of vector C, |C| = 15.0 m, and its angle counterclockwise from the -x direction, which is 20°.
To find the vector B, we need to use vector addition to subtract vector A from vector C, as follows: B = C - A.
(a) To find the magnitude of vector B, we can use the Pythagorean theorem, which states that the magnitude of the vector is equal to the square root of the sum of the squares of its components.
So we have:
|B|^2 = |C|^2 + |A|^2
|B|^2 = (15.0 m)^2 + (13.1 m)^2
|B|^2 = 225 m^2 + 171.61 m^2
|B|^2 = 396.61 m^2
Taking the square root of both sides, we find:
|B| = √(396.61 m^2) ≈ 19.9 m
Therefore, the magnitude of vector B is approximately 19.9 m.
(b) To find the direction of vector B, we can use trigonometry. Since we are given the angles of vector A and vector C, we can find the angle of vector B relative to the +x direction.
First, let's find the angle of vector A relative to the +x direction:
θ_A = 180° - 49° = 131°
Next, let's find the angle of vector C relative to the +x direction:
θ_C = 180° + 20° = 200°
Now, let's find the angle of vector B relative to the +x direction by subtracting the angle of vector A from the angle of vector C:
θ_B = θ_C - θ_A
θ_B = 200° - 131°
θ_B = 69°
Therefore, the direction of vector B relative to the +x direction is 69°.
So, the answers are:
(a) The magnitude of vector B is approximately 19.9 m.
(b) The direction of vector B relative to the +x direction is 69°.