Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
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Chapter 3, Problem 2P

(a)

To determine

The magnitude and direction of A+B.

(a)

Expert Solution
Check Mark

Answer to Problem 2P

The vector A+B has magnitude 0.73units_ and it is directed along the +x-direction_.

Explanation of Solution

Given that the vector A is directed along the positive x-axis and has magnitude 1.73units, and the vector B is directed along the negative x-axis and has magnitude 1.00unit.

Let us consider the +x-direction be to right.

The vector diagram of the vectors A, B, and A+B is shown in Figure 1.

Physics, Chapter 3, Problem 2P , additional homework tip  1

Conclusion:

From the vector diagram in Figure 1 the magnitude of the resultant vector A+B is obtained as,

A+B=1.73units1.00unit=0.73units

As shown in the vector diagram, the direction of A+B is in the +x-direction.

Therefore, the vector A+B has magnitude 0.73units_ and it is directed along the +x-direction_.

(b)

To determine

The magnitude and direction of AB.

(b)

Expert Solution
Check Mark

Answer to Problem 2P

The vector AB has magnitude 2.73units_ and it is directed along the +x-direction_.

Explanation of Solution

Given that the vector A is directed along the positive x-axis and has magnitude 1.73units, and the vector B is directed along the negative x-axis and has magnitude 1.00unit.

Let us consider the +x-direction be to right.

The vector diagram of the vectors A, B, and AB is shown in Figure 2.

Physics, Chapter 3, Problem 2P , additional homework tip  2

Conclusion:

From the vector diagram in Figure 2 the magnitude of the resultant vector AB is obtained as,

AB=1.73units+1.00unit=2.73units

As shown in the vector diagram, the direction of AB is in the +x-direction.

Therefore, the vector AB has magnitude 2.73units_ and it is directed along the +x-direction_.

(c)

To determine

The magnitude and direction of BA.

(c)

Expert Solution
Check Mark

Answer to Problem 2P

The vector BA has magnitude 2.73units_ and it is directed along the x-direction_.

Explanation of Solution

Given that the vector A is directed along the positive x-axis and has magnitude 1.73units, and the vector B is directed along the negative x-axis and has magnitude 1.00unit.

Let us consider the +x-direction be to right.

The vector diagram of the vectors A, B, and BA is shown in Figure 3.

Physics, Chapter 3, Problem 2P , additional homework tip  3

Conclusion:

From the vector diagram in Figure 3 the magnitude of the resultant vector BA is obtained as,

BA=1.00unit+1.73units=2.73units

As shown in the vector diagram, the direction of BA is in the x-direction.

Therefore, the vector BA has magnitude 2.73units_ and it is directed along the x-direction_.

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