Vector Addition and Subtraction: Analytical Methods Quiz

PDF page 167: For the analytical method of vector addition and subtraction, we use some simple geometry and trigonometry, instead of using a ruler and protractor as we did for graphical methods. However, the graphical method will still come in handy to visualize the problem by drawing vectors using the head-to-tail method. The analytical method is more accurate than the graphical method, which is limited by the precision of the drawing. For a refresher on the definitions of the sine, cosine, and tangent of an angle, see Figure 5.17.

PDF page 167: For the analytical method of vector addition and subtraction, we use some simple geometry and trigonometry, instead of using a ruler and protractor as we did for graphical methods. However, the graphical method will still come in handy to visualize the problem by drawing vectors using the head-to-tail method. The analytical method is more accurate than the graphical method, which is limited by the precision of the drawing. For a refresher on the definitions of the sine, cosine, and tangent of an angle, see Figure 5.17.

PDF page 176: b. The analytical method is more accurate than the graphical method, because the latter involves some extensive

PDF page 167: For the analytical method of vector addition and subtraction, we use some simple geometry and trigonometry, instead of using a ruler and protractor as we did for graphical methods. However, the graphical method will still come in handy to visualize the problem by drawing vectors using the head-to-tail method. The analytical method is more accurate than the graphical method, which is limited by the precision of the drawing. For a refresher on the definitions of the sine, cosine, and tangent of an angle, see Figure 5.17.

PDF page 176: d. The analytical method is more accurate than the graphical method, because the latter is limited by the precision of the

PDF page 168: Since, by definition, , we can find the length x if we know h and by using . Similarly, we can find the length of y by using . These trigonometric relationships are useful for adding vectors. When a vector acts in more than one dimension, it is useful to break it down into its x and y components. For a two-dimensional vector, a component is a piece of a vector that points in either the x- or y-direction. Every 2-d vector can be expressed as a sum of its x and y components.

PDF page 176: a. A component is a piece of a vector that points in either the x or y direction.

PDF page 168: Since, by definition, , we can find the length x if we know h and by using . Similarly, we can find the length of y by using . These trigonometric relationships are useful for adding vectors. When a vector acts in more than one dimension, it is useful to break it down into its x and y components. For a two-dimensional vector, a component is a piece of a vector that points in either the x- or y-direction. Every 2-d vector can be expressed as a sum of its x and y components.

PDF page 168: These vectors form a right triangle.

PDF page 168: produce it. In this example, and form a right triangle, meaning that the angle between them is 90 degrees. This is a

PDF page 168: produce it. In this example, and form a right triangle, meaning that the angle between them is 90 degrees. This is a

PDF page 170: Since this is a right triangle, the Pythagorean theorem (x + y = h ) for finding the hypotenuse applies. In this case, it becomes

PDF page 174: Now we can find the magnitude of the resultant by using the Pythagorean theorem

PDF page 174: Discussion This example shows vector addition using the analytical method. Vector subtraction using the analytical method is very similar. It is just the addition of a negative vector. That is, . The components of – are the negatives of the are components of . Therefore, the x- and y-components of the resultant

PDF page 169: Then A = 10.3 blocks and , so that

PDF page 169: This magnitude indicates that the walker has traveled 9 blocks to the east—in other words, a 9-block eastward displacement. Similarly,

PDF page 171: Figure 5.23 To add vectors and first determine the horizontal and vertical components of each vector. These are the dotted

PDF page 173: We will solve for these components and then add them in the x-direction and y-direction to find the resultant. Solution