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Chapter 3: Q13P (page 57)

A person desires to reach a point that is3.40kmfrom her present location and in a direction that is3.50掳north of east. However, she must travel along streets that are oriented either north鈥搒outh or east鈥搘est. What is the minimum distance she could travel to reach her destination?

Short Answer

Expert verified

The minimum distance traveled to reach destination is4.47km

Step by step solution

01

To understand the concept of scalar projection

This problem refers to scalar projection. In Cartesian coordinates, scalar components are scalar projections in the directions of the coordinate axes. Using this concept, the distance can be calculated by finding the components and adding those components.

The components can be written as

dx=dcos胃dy=dsin胃

Therefore the minimum distance D is given by the following formula.

D=dx+dy=dcos胃+dsin胃i

02

To find the minimum distance traveled

Given are,

d=3.40km胃=35.0掳

Substituting the above values in equation (i), the minimum distance D can be written as,

D=3.40脳cos35.0+3.40脳sin35.5

Thus, D=4.47km

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Most popular questions from this chapter

In Fig. , a cube of edge length a sits with one corner at the origin of an xyz coordinate system. A body diagonal is a line that extends from one corner to another through the center. In unit-vector notation, what is the body diagonal that extends from the corner at (a) coordinates (0,0,0), (b) coordinates (a,0,0), (c) coordinates (0,a,0), and (d) coordinates (a,a,0)? (e) Determine the angles that the body diagonals make with the adjacent edges. (f) Determine the length of the body diagonals in terms of a.

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A particle undergoes three successive displacements in a plane, as follows:d1鈫�, 4.00 m southwest; then d2鈫�, 5.00 m east; and finally d3鈫�, 6.00 m in a direction 60掳north of east. Choose a coordinate system with the y axis pointing north and the x axis pointing east. What are (a) the x component and (b) the y component of d1鈫�? What are (c) the x component and (d) the y component of d2鈫�? What are (e) the component and (f) the y component of d3鈫�? Next, consider the net displacement of the particle for the three successive displacements. What are (g) the x component, (h) the y component, (i) the magnitude, and ( j) the direction of the net displacement? If the particle is to return directly to the starting point, (k) how far and (l) in what direction should it move?
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