ssrs code 39

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The process for adding vectors works even when the vectors do not point along the same straight line If you are solving one of these two-dimensional problems graphically, you will need to use a protractor, both to draw the vectors at the correct angles and also to measure the direction and magnitude of the resultant vector You can add vectors by placing them tip-to-tail and then drawing the resultant of the vector by connecting the tail of the first vector to the tip of the second vector, as shown in Figure 5-2 Figure 5-2a shows the two forces in the free-body diagram In Figure 5-2b, one of the vectors has been moved so that its tail is at the same place as the tip of the other vector Notice that its length and direction have not changed Because the length and direction are the only important characteristics of the vector, the vector is unchanged by this movement This is always true: if you move a vector so that its length and direction are unchanged, the vector is unchanged Now, as in Figure 5-2c, you can draw the resultant vector pointing from the tail of the first vector to the tip of the last vector and measure it to obtain its magnitude Use a protractor to measure the direction of the resultant vector Sometimes you will need to use trigonometry to determine the length or direction of resultant vectors Remember that the length of the hypotenuse of a right triangle can be found by using the Pythagorean theorem If you were adding together two vectors at right angles, vector A pointing north and vector B pointing east, you could use the Pythagorean theorem to find the magnitude of the resultant, R Pythagorean Theorem R2 A2 B2

In a utility application with only one window, you might want to uncheck this box so that the window can t be closed If this box is unchecked, both the red close button in the window s title bar and the Close menu item will be disabled If you allow the window to be closed, you should provide a way to make the window visible again Alternatively, if your application is a utility that consists of only one window, it is acceptable to have the application quit when the window is closed Later on in this chapter, we ll configure our application to quit when this window is closed, so leave the Close checkbox as it is In later chapters, you ll learn how to make closed windows visible again.

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Figure 5-2 Add vectors by placing them tip-to-tail and drawing the resultant from the tail of the first vector to the tip of the last vector

If vector A is at a right angle to vector B, then the sum of the squares of the magnitudes is equal to the square of the magnitude of the resultant vector

If the two vectors to be added are at an angle other than 90 , then you can use the law of cosines or the law of sines Law of Cosines R2 A2 B2 2AB cos

The square of the magnitude of the resultant vector is equal to the sum of the magnitudes of the squares of the two vectors, minus two times the product of the magnitudes of the vectors, multiplied by the cosine of the angle between them

R A B sin sin a sin b The magnitude of the resultant, divided by the sine of the angle between two vectors, is equal to the magnitude of one of the vectors divided by the angle between that component vector and the resultant vector

The Minimize checkbox controls whether the window can be minimized to the dock using the yellow button in the window s title bar or from selecting Minimize from the Window menu As a general rule, windows should be able to be minimized There are exceptions to this, such as utility windows that are only visible when your application is front-most, but the vast majority of the time you should leave this checked..

Finding the Magnitude of the Sum of Two Vectors Find the magnitude of the sum of a 15-km displacement and a 25-km displacement when the angle between them is 90 and when the angle between them is 135

8:

Sketch the two displacement vectors, A and B, and the angle between them Known:

Unknown:

90 135 R

When the angle is 90 , use the Pythagorean theorem to find the magnitude of the resultant vector R 2 A2 B 2 R A2 B2 (25 km)2 (15 km)2 Substitute A 25 km, B 15 km 29 km When the angle does not equal 90 , use the law of cosines to find the magnitude of the resultant vector R 2 A2 B 2 2AB(cos 2) R A2 B2 2AB(cos (15 km)2

2(25 km)(15 km)(cos 135 )

CHAPTER 3: Lights, Camera Actions! (and Outlets, Too)

15 km,

135

Are the units correct Each answer is a length measured in kilometers Do the signs make sense The sums are positive Are the magnitudes realistic The magnitudes are in the same range as the two combined vectors, but longer This is because each resultant is the side opposite an obtuse angle The second answer is larger than the first, which agrees with the graphical representation

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