Calculating the Magnitude of Vector B with Trig | Homework Help

• Ampere
In summary, the magnitude of vector B can be calculated using trigonometry and the resolution of vector components. The resulting magnitude is 13.20 units, which is also confirmed by another member's calculation using the cosine law. The given choices for the magnitude of B may be incorrect.

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

1 person
Ampere said:

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?

1 person
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.

Ampere said:
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.

Awesome, thanks.

Dick said:
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

Dick said:
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

1. What is a vector?

A vector is a mathematical object that has both magnitude (size) and direction. It is commonly represented by an arrow, with the length of the arrow indicating the magnitude and the direction of the arrow indicating the direction.

2. What is the difference between a vector and a scalar?

A vector has both magnitude and direction, while a scalar only has magnitude. For example, velocity is a vector because it has both speed (magnitude) and direction. Temperature, on the other hand, is a scalar because it only has magnitude.

3. How are vectors used in science?

Vectors are used in many areas of science, including physics, engineering, and computer science. They can be used to describe quantities such as force, velocity, and acceleration, and are crucial in understanding motion and other physical phenomena.

4. What is the difference between a vector and a matrix?

A vector is a one-dimensional array of numbers, while a matrix is a two-dimensional array of numbers. Vectors are often used to represent quantities like position or velocity, while matrices are used to represent systems of equations or transformations.

5. How do you add and subtract vectors?

To add or subtract vectors, you simply add or subtract the corresponding components of the vectors. For example, to add two 2D vectors (a,b) and (c,d), you would add their x-components (a+c) and their y-components (b+d) to get the resulting vector (a+c, b+d). This follows the commutative and associative properties of addition.