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 7P

Figure 3-33 shows two vectors, A and B , whose magnitudes are A = 6.8 units and B = 5.5 units. Determine C if (a) C = A + B , (b) C = A B , (c) C = B A . Give the magnitude and direction for each.

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Chapter 3, Problem 7P, Figure 3-33 shows two vectors, A  and B  , whose magnitudes are A=6.8 units and B=5.5 units.

Figure 3-33

Problem 7.

Expert Solution
Check Mark
To determine

Section 1:

C=A+B

Answer to Problem 7P

Solution:

Vector C has a magnitude of 1.3 units and has a direction of 0° to the East. has a magnitude of 1.3 units and has a direction of 0° to the east.

Explanation of Solution

Given:

The magnitude |A| of vector A is 6.8 units and the magnitude |B| of vector B is 5.5 units.

Formula used:

According to the figure, vectors A and B only have x-component, in effect:

       A=Axi^=|A|.cos(0°)i^=|A|i^                                                                                        (1)

This vector points to the right, while that vector Bpoints to the left, therefore:

       B=Bxi^=|B|cos(180˚)i^=|B|i^                                                                                  (2)

Calculation:

Replacing data given in equations (1)and (2)we obtain:

       A=6.8 units i^                                                                                                                      (3)

and

       B=5.5 units i^                                                                                                                   (4)

Now, vector C is:

       C=A+B=6.8 units i^+(=5.5 units i^)=1.3 units i^                                      (5)

Therefore, vector C has a magnitude of 1.3 units and has a direction of 0° points to the East.

Expert Solution
Check Mark
To determine

Section 2:

C=A-B

Answer to Problem 7P

Solution:

Vector C has a magnitude of 12.3 units and has a direction of 0° to the East.

Explanation of Solution

Given:

Results (3)and (4).

Formula used:

The vector C can be obtained using:

       C=AB                                                                                                                              (6)

Inserting (3)and (4)into (6)we have:

       C=6.8 units i^(5.5 units)i^                                                                                     (7)

Solving we obtain:

      C=12.3 units i^                                                         (8)

Therefore, vector C

has a magnitude of 12.3 units and has a direction of 0° to the East.

Expert Solution
Check Mark
To determine

Section 3:

C=BA

Answer to Problem 7P

Solution:

Vector C has a magnitude of 12.3 units and has a direction of 180° to the West.

Explanation of Solution

Explanation.:

Given:

Results (3)and (4).

Formula used:

The vector C can be obtained using:

      C=BA                                                                                                                              (9)

Inserting (3)and (4)into (9)we have:

      C=5.5 unitsi^6.8 units i^                                                                                     (10)

Solving we obtain:

      C=12.3 units i^(11)

Therefore, vector C

has a magnitude of 12.3 units and has a direction of 180° to the West.

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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