Question

ruth sets out to visit her friend ward, who lives 20 mi north and 100 mi east of her. she starts by driving east, but after 40 mi she comes to a diner that takes her 15 mi south before going east again. she then drives east for 8 mi and runs out of gas, so ward flies there in his small plane to get her. part a what is ward’s displacement vector? (give your answer in component form, using a coordinate system in which the y - axis points north. express your answers in miles and separated by a comma.) view available hint(s) hint 1. how to approach the problem use the point where ruth starts her travel as the origin. find vectors whose components are easy to determine and whose sum or difference equals the displacement vector. use them to find the components of the displacement vector

Explanation:

Step1: Determine the east - west (x - component) displacement

Ward lives 100 mi east of Ruth's starting point. The x - component (east - west) of the displacement vector is the eastward distance, so \(F_x = 100\) miles (since east is the positive x - direction in a coordinate system where we can define east as x - positive and north as y - positive).

Step2: Determine the north - south (y - component) displacement

Ward lives 20 mi north of Ruth's starting point. The y - component (north - south) of the displacement vector is the northward distance. Even though Ruth drove south at one point, the displacement vector from Ruth's start to Ward's house is based on the final position of Ward relative to Ruth's start. So \(F_y=20\) miles (since north is the positive y - direction).

Answer:

100, 20