Final answer:
The question involves finding the resultant vector from a combination of vectors and expressing it using polar coordinates. The resultant vector R→ has a magnitude of 50.8 m and a direction of 5.47° south of east. Analytical methods involve decomposing vectors into components, summing them, and then using the Pythagorean theorem and arctangent to find the magnitude and direction of R→.
Step-by-step explanation:
The student's question involves adding vectors to form a resultant vector and expressing it in polar vector representation. To find the resultant vector (R→), one must graphically or analytically combine the given vectors. According to Figure 3.17, the resultant vector has a magnitude of 50.8 m and a direction of 5.47° south of east. This can be expressed as R = 50.8 m at an angle of θ = 5.47° south of east.
To determine the magnitude and direction of the resultant vector analytically, one would break down the given vectors into their x (horizontal) and y (vertical) components, add the components from each vector, and then use the Pythagorean theorem to find the magnitude of the resultant vector. The direction can be found by calculating the arctangent of the ratio of the y-component to the x-component. Remember, this direction should be measured from the positive x-axis (eastward axis), and adjustments should be made based on the vector being south of the eastward axis.
Since the question mentions the vectors having a particular magnitude and direction, such as Vector A with magnitude 53.0 m and direction 20.0° north of the x-axis, and Vector B with magnitude 34.0 m and direction 63.0⁰ north of the x-axis, the student should apply the same analytical approach to combine these vectors, ensuring that all angles are measured with respect to the positive x-axis and using the proper signs for each component based on their direction (north or south of the x-axis).