Question

When given a magnitude and degree in bearings of two vectors and asked for the combined magnitude and direction angle--------------------

A. Magnitude: 13, Direction Angle: 90^∘.
B. Magnitude: 12, Direction Angle: 60^∘.
C. Magnitude: 14, Direction Angle: 135^∘.
D. Magnitude: 15, Direction Angle: 30^∘.

Answer 1

To find the combined magnitude and direction of two vectors, resolve each vector into its components, then add them to determine the resultant vector's components, and finally calculate its magnitude and direction.

Step-by-step explanation:

When we want to combine the magnitudes and direction angles of two vectors, we are typically dealing with vector addition. The combined magnitude and direction can be found by breaking each vector into its horizontal (x) and vertical (y) components, adding the corresponding components together, and then using the Pythagorean theorem and trigonometry to find the resultant vector.

To find the components, we can use the following equations:

• Ax = A * cos(θA)
• Ay = A * sin(θA)
• Bx = B * cos(θB)
• By = B * sin(θB)

After finding the components, we add them to get the resultant vector's components:

• Rx = Ax + Bx
• Ry = Ay + By

The magnitude (R) and direction angle of the resultant vector (R) are found using:

• Magnitude: R = sqrt(Rx^2 + Ry^2)
• Direction angle: θR = atan2(Ry, Rx)

It's important to note that 'atan2' accounts for the quadrant in which the resultant vector R lies.

For example, if we have a vector A with a magnitude of 53.0 m and direction 20.0° north of the x-axis, and a vector B with a magnitude of 34.0 m and direction 63.0⁰ north of the x-axis, we would calculate the combined magnitude and direction using these steps.

This involves using analytical methods such as resolving each vector into its components and then combining these to find the resultant vector.