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Chrome File Edit View History Bookmarks People Window Help 4) 55% [ Mon 2:15 PM a //LI WileyPLUS d Secure https://edugen.wileyplus.com/edugen/student/mainfr.uni !) Jenna Apps Chromecast WileyPLUS Cutnell,Phyaics,10 General Physics 1 (Fall 2017) (APHY105) Home Read, Study & Practice Gradebook ORION Downloadable cTextbook Assignment> Open Assignment FULL SCREEN PRINTER VERSION BACK NEXT ASSIGNMENT RESOURCES Chapter 01, Problem 50 Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 18.0 m, B = 11.0 m, C-13.0 m, and D = 22.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs when these vectors are added together. Specify the direction as a positive (counterclockwise) angle from the +x axis. Homework 5 (Chapters 1-3) hapter 01, Problem 5 oble GO 35 0.0 Review Results by St (a) Number (b) Number Click if you would like to Show Work for this question: Units Units Open Show Work

Explanation / Answer

All the vectors can be resolved into their x and y components: x=rcos, y=rsin where r is the magnitude and is the angle of the vector with respect to the positive x-axis.

These components can then be added together to form the x and y components of the resultant.

A: r=18, =160°
B: r=11, =90°
C: r=13, =215°
D: r=22, =310°

The x & y components of the resultant is equal to the sum of the x & y components of each vector

x=component of resultant = 18cos160° + 11cos90° + 13cos215° + 22cos310°
y=component of resultant = 18sin160° + 11sin90° + 13sin215° + 22sin310°

x-component = -13.42
y-component = -7.15

Therefore the resultant vector will have magnitude {(-13.42)² + (-7.15)²} = 15.2
and direction = arctan(-7.15/-13.42) = 28.04°

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