Question

A man hikes 3.2 miles at 32° S of W and then turns to walk another 2.7 miles 46° N of E. What is his displacement?

a) 5.9 miles at 14° S of W
b) 6.2 miles at 78° N of E
c) 4.5 miles at 32° S of W
d) 2.7 miles at 46° N of E

Answer 1

The displacement of the man hiking can be found using vector addition of his directional walks. The vectors are broken down into their east-west and north-south components, summed up, and then the resultant vector magnitude and direction are determined. Specific diagrams or context needed for an exact answer were not provided.

Step-by-step explanation:

To determine the man's displacement, we need to consider the given vectors and apply the concept of vector addition. Displacement is a vector quantity that has both magnitude and direction. The first part of the hike is 3.2 miles at 32° South of West, and the second part is 2.7 miles at 46° North of East. Unfortunately, without knowing the specific question figures and the context (such as Figure 3.47 mentioned in the additional information), it's not possible to provide an exact answer to the student's question.

Nonetheless, in general, the displacement can be found by breaking down these vectors into their east-west (horizontal) and north-south (vertical) components and then combining them to find the resultant vector. Each component is calculated using trigonometric functions (sine and cosine).

After finding the components, they are summed to find the total displacement vector. Finally, the magnitude and direction of the resultant vector are determined algebraically. The direction is usually given in terms of degrees from the north (measured clockwise) or from the east (measured counterclockwise).