University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 1 - Units, Physical Quantities, and Vectors - Problems - Exercises - Page 29: 1.38

Answer

a) A= 1.23i + 3.38j B= -2.078i + (-1.2)j b) 12.0i + 14.9j c) 19.2 m, 51.2°

Work Step by Step

a) A= 3.60 m Ax= Acos(70) = 3.60 x cos(70) = 1.23 m= 1.23i Ay= Asin(70) = 3.60 x sin(70) = 3.38 m= 3.38j B= 2.4. m Bx= Bcos(30)= 2.4 x cos(30) = -2.078 m= -2.08i By= Bsin(30)= 2.4 x sin(30) = -1.20 m = -1.20j b) C= 3(A) - 4(B) C= 3(1.23i + 3.38j) - 4((-2.08i) + (-1.2j)) C= 3.69i + 10.14j + 8.32i + 4.8j C= 12.01i + 14.94j = 12.0i + 14.9j c) C= ((12.01)^2 + (14.94)^2)^1/2= 19.16 m = 19.2 m \theta= Tan^-1(14.94/12.01) = 51.2°
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