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 5P

V is a vector 24.8 units in magnitude and points at an angle of 23.4° above the negative axis, (a) Sketch this vector, (b) Calculate Vxand Vy. (c) Use Vxand Vy.andVy to obtain (again) the magnitude and direction of V [Note: Part (c) is a good way to check if you've resolved your vector correctly.]

Expert Solution & Answer
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Solution

  1. Sketch of the vector |V|=24.8units and points at an angle of θ=23.4o above the negative x -axis
  2. Vx and Vy
  3. The magnitude |V| and direction θ using Vx and Vy .

Solution:

  1. The sketch of the vector is shown below:
  2.   Physics: Principles with Applications, Chapter 3, Problem 5P , additional homework tip  1

  3. The components Vx and Vy are -22.8 units and 9.85 units respectively.
  4. The magnitude |V| is 24.8 units and the direction θ=23.4o above the negative x-axis.

Explanation:

The magnitude of the vector |V|=24.8units and points at an angle of θ=23.4o above the negative x-axis

In this case, the direction θ is given above negative x-axis, this angle is counted from the negative-axis as follows:

  Physics: Principles with Applications, Chapter 3, Problem 5P , additional homework tip  2

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:

Substitute the values

  Vx=24.8cos( 180o 23.4o)Vx=22.8unitsVy=24.8sin( 180o 23.4o)Vy=9.85units

The magnitude of vector can be obtained by:

  |V|=( V x 2 )+ ( V y )2|V|= ( 22.8 )2+ ( 9.85 )2|V|=24.8

And, the direction θ is defined as:

  θ=tan1(VyVx)

  θ=tan1(9.8522.8)=23.4o

05:25

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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