Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 3, Problem 12P

For the vectors shown in Fig. 3—35, determine (a) B 3 A , (b) 2 A 3 B  + 3 C

Expert Solution & Answer
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Solution

To Determine:

  1. B3A
  2. R=2A3B+2C

Solution:

  1. The magnitude of resultant vector B3A is 137.1 with a direction of 196.9˚ counterclockwise from +x-axis.
  2. The magnitude of resultant vector R=2A3B+2C is 149.7 with a direction of 324.6˚ counterclockwise from +x-axis.

Explanation:

Given: The magnitude |A| is 44.0 with a direction θ'A of 28.0˚ counterclockwise from the positive x -axis. For |B| the magnitude is 26.5with a direction θ'B of 56.0˚ clockwise from the negative x -axis and the magnitude of |C| is 31.0 with a direction of θ'C of 270˚ on the negative y-axis.

Formula used:

The x -component Vx of vector V is defined as:

  Vx=|V|cosθ

The y-component of Vy vector V is defined as:

  Vy=|V|sinθ

Where:

  • |V| is the magnitude of the vector V
  • θ is the direction of the vector V measured respect to the positive x -axis counter-clockwise.

The magnitude of vector can be obtained by:

  |V|=(Vx2)+( V y )2

And, the direction θ is defined as:

  θ=tan1(VyVx)

Calculation:Section 1: x -component of A

  Ax=44cos28o=38.8

y -component of A

  Ay=44sin28o=20.6

x -component of B

  Bx=26.5cos( 180o 56o)=14.8

y -component of B

  By=26.5sin( 180o 56o)=22

Therefore, the x-component of B3A is:

  Bx3Ax=14.83(38.8)=131.2

Similarly, the y-component of B3A is:

  By3Ay=223(20.6)=39.8

Therefore, the magnitude of B3A is:

  |B3A|= ( 131.2 )2+ ( 39.8 )2=137.1

  θ=tan1( 39.8 131.2)=16.9=180o+16.9o=196.9o

Therefore, the vector B3A has a magnitude of 137.1 with a direction of 196.9˚ counterclockwise from + x -axis.

Section 2: x -component of C

  Cx=31cos( 270o)=0

y -component of C

  Cy=31sin( 270o)=31

  R=2A3B+2C

  Rx=2Ax3Bx+2Cx=2(38.8)3(14.8)+2(0)=122Ry=2Ay3By+2Cy=2(20.6)3(22)+2(31)=86.8

  |R|= ( 122 )2+ ( 86.8 )2=149.7

  θ=tan1( 86.8 122)=35.4=360o35.4o=324.6o

Conclusion:

The magnitude of resultant vector B3A is 137.1 with a direction of 196.9˚ counterclockwise from +x-axis.

The magnitude of resultant vector R=2A3B+2C is 149.7 with a direction of 324.6˚ counterclockwise from +x-axis.

14:47

Chapter 3 Solutions

Physics: Principles with Applications

Ch. 3 - Prob. 11QCh. 3 - Prob. 12QCh. 3 - Prob. 13QCh. 3 - A projectile is launched at an upward angle of 300...Ch. 3 - Prob. 15QCh. 3 - Two cannonballs, A and B, are fired from the...Ch. 3 - 18. A person sitting in an enclosed train car,...Ch. 3 - Prob. 18QCh. 3 - Prob. 19QCh. 3 - Prob. 20QCh. 3 - A car is driven 225 km west and then 98 km...Ch. 3 - A delivery truck travels 21 blocks north, 16...Ch. 3 - If Vx=9.80 units and Vy=6.40 units, determine the...Ch. 3 - Graphically determine the resultant of the...Ch. 3 - V is a vector 24.8 units in magnitude and points...Ch. 3 - Vector V is 6.6 using long and points along the...Ch. 3 - Figure 3-33 shows two vectors, A and B , whose...Ch. 3 - Prob. 8PCh. 3 - Three vectors are shown in Fig. 3-35 Q. Their...Ch. 3 - (a) given the vectors A and B shown in Fig. 3-35,...Ch. 3 - Determine the vector AC , given the vectors A and...Ch. 3 - For the vectors shown in Fig. 3—35, determine (a)...Ch. 3 - Prob. 13PCh. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Prob. 16PCh. 3 - Prob. 17PCh. 3 - 17. (l) A tiger leaps horizontally from a...Ch. 3 - 18. (l) A diver running 2.5 m/s dives out...Ch. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28PCh. 3 - Prob. 29PCh. 3 - Prob. 30PCh. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Prob. 37PCh. 3 - Prob. 38PCh. 3 - Prob. 39PCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Prob. 44PCh. 3 - Prob. 45PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48PCh. 3 - Prob. 49PCh. 3 - Prob. 50PCh. 3 - Prob. 51PCh. 3 - Prob. 52PCh. 3 - Prob. 53GPCh. 3 - Prob. 54GPCh. 3 - Prob. 55GPCh. 3 - Prob. 56GPCh. 3 - Prob. 57GPCh. 3 - Prob. 58GPCh. 3 - Prob. 59GPCh. 3 - Prob. 60GPCh. 3 - Prob. 61GPCh. 3 - Prob. 62GPCh. 3 - Prob. 63GPCh. 3 - Prob. 64GPCh. 3 - Prob. 65GPCh. 3 - Prob. 66GPCh. 3 - Prob. 67GPCh. 3 - Prob. 68GPCh. 3 - Prob. 69GPCh. 3 - Prob. 70GPCh. 3 - Prob. 71GPCh. 3 - Prob. 72GPCh. 3 - Prob. 73GPCh. 3 - Prob. 74GPCh. 3 - Prob. 75GP
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