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Fundamentals Of Physics
Found in: Page 57
Fundamentals Of Physics

Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

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Short Answer

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

The minimum distance traveled to reach destination is4.47 km

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: 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=d cos θdy=d sin θ

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

D=dx+dy=d cosθ+d sinθi

Step 2: To find the minimum distance traveled

Given are,

d=3.40 kmθ=35.0°

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

D=3.40×cos35.0+3.40×sin35.5

Thus, D=4.47 km

Most popular questions for Physics Textbooks

If B→ is added to A→, the result is 6.0i^+1.0j^ . If B→is subtracted from role="math" localid="1656310989938" A→ , the result is -4.0i^+7.0j^. What is the magnitude of role="math" localid="1656311031101" A→?

For the vectors in Fig. 3-32, with a=4, b=3, and c=5 , what are (a) the magnitude and (b) the direction of a→×b→, (c) the magnitude and (d) the direction of a→×c→, and (e) the magnitude and (f) the direction of b→×c→? (The z-axis is not shown)

Here are three displacements, each measured in meters: d→1=4.0i⏜+5.0j⏜-6.0k⏜,d→2=-1.0i⏜+2.0j⏜+3.0k⏜ ,andd→3=4.0i⏜+3.0j⏜+2.0k⏜. (a) What is r→=d→1+d→2+d→3 ? (b) What is the angle betweenr→ and the positive z axis? (c) What is the component of d1 along the direction of d→2 (d) What is the component of d→1 that is perpendicular to the direction of d2→ and in the plane of role="math" localid="1658465314757" d→1and d→2 (Hint: For (c), consider Eq 3-20. and Fig, 3-18; for (d), consider Eq.3-24.)

Vectors A→ and B→ lie in an xy plane. A→ has magnitude 8.00 and angle 130°; has components localid="1657001111547" Bx=-7.72 and By=9.20. What are the angles between the negative direction of the y axis and (a) the direction of A→ , (b) the direction of the product A→×B→, and (c) the direction of localid="1657001453926" A→×(B→+3.00)k⏜?

A room has dimensions 3.00 m (height) ×3.70×4.30 m. A fly starting at one corner flies around, ending up at the diagonally opposite corner. (a) What is the magnitude of its displacement? (b) Could the length of its path be less than this magnitude? (c) Greater? (d) Equal? (e) Choose a suitable coordinate system and express the components of the displacement vector in that system in unit-vector notation. (f) If the fly walks, what is the length of the shortest path? (Hint: This can be answered without calculus. The room is like a box. Unfold its walls to flatten them into a plane.)
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