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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find the magnitude of the resultant force and the angle it makes with the positive x-axis.

33. Chapter 12.2, Problem 32E, Find the magnitude of the resultant force and the angle it makes with the positive x-axis. 33.

To determine

Solution: The magnitude of resultant force and angle with positive x-axis are 28.7lb_ and 12.4°_ respectively.

Explanation

Given:

The magnitude of first vector as 20 lb and a angle with positive x-axis as 45° and the magnitude of second vector as 16 lb and angle with positive x-axis as 30° .

Formula:

Write the expression for vector in terms of horizontal and vertical components.

F=|F|cosθi+|F|sinθj (1)

Here,

|F| is magnitude of vector F.

Write the expression for resultant vector of two vectors F1 and F2 (F) .

F=F1+F2 (2)

Write the expression for magnitude of vector F1i+F2j .

|F|=F12+F22 (3)

Write the expression for tanθ of a vector F.

tanθ=F2F1 (4)

Substitute 20 lb for |F| , and 45° for θ in equation (1),

F1=(20lb)cos(45°)i+(20lb)sin(45°)j=(20lb)(12)i+(20lb)(12)j=102i+102jlb

Substitute 16 lb for |F| , and 30° for θ in equation (1),

F2=(16lb)cos(30°)i+(16lb)sin(30°)j=(16lb)(32)i+(16lb)(12)j=83

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Chapter 12 Solutions

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P-48ESect-12.6 P-49ESect-12.6 P-50ESect-12.6 P-51ESect-12.6 P-52ECh-12 P-1RCCCh-12 P-2RCCCh-12 P-3RCCCh-12 P-4RCCCh-12 P-5RCCCh-12 P-6RCCCh-12 P-7RCCCh-12 P-8RCCCh-12 P-9RCCCh-12 P-10RCCCh-12 P-11RCCCh-12 P-12RCCCh-12 P-13RCCCh-12 P-14RCCCh-12 P-15RCCCh-12 P-16RCCCh-12 P-17RCCCh-12 P-18RCCCh-12 P-19RCCCh-12 P-1RQCh-12 P-2RQCh-12 P-3RQCh-12 P-4RQCh-12 P-5RQCh-12 P-6RQCh-12 P-7RQCh-12 P-8RQCh-12 P-9RQCh-12 P-10RQCh-12 P-11RQCh-12 P-12RQCh-12 P-13RQCh-12 P-14RQCh-12 P-15RQCh-12 P-16RQCh-12 P-17RQCh-12 P-18RQCh-12 P-19RQCh-12 P-20RQCh-12 P-21RQCh-12 P-22RQCh-12 P-1RECh-12 P-2RECh-12 P-3RECh-12 P-4RECh-12 P-5RECh-12 P-6RECh-12 P-7RECh-12 P-8RECh-12 P-9RECh-12 P-10RECh-12 P-11RECh-12 P-12RECh-12 P-13RECh-12 P-14RECh-12 P-15RECh-12 P-16RECh-12 P-17RECh-12 P-18RECh-12 P-19RECh-12 P-20RECh-12 P-21RECh-12 P-22RECh-12 P-23RECh-12 P-24RECh-12 P-25RECh-12 P-26RECh-12 P-27RECh-12 P-28RECh-12 P-29RECh-12 P-30RECh-12 P-31RECh-12 P-32RECh-12 P-33RECh-12 P-34RECh-12 P-35RECh-12 P-36RECh-12 P-37RECh-12 P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

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