assignment 9

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

Thanks for noting that. I'm not sure how the 164.106.222.236 address is still working, but I'm glad it is.

Sometimes the number generators malfunction; rather I should say that the programmer (that's me) managed to mess up in such a way that the right numbers don't always show up.

I'll check into that one.

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13:14:00 `q001. Sketch the points (2,3) and (9,14) on a set of coordinate axes. Give the x and the y displacements from (2,3) to (9,14).

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RESPONSE --> x displacement 7 y displacement 11

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13:14:34 As shown in Figure 75, the x displacement is from 2 to 9, a displacement of 9 - 2 = 7, while the y displacement is from 3 to 14, a displacement of 14 - 3 = 11. The arrows represent the direction of the displacements, from the initial point (2, 3) to the terminal point (9, 14).

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RESPONSE --> check

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13:16:42 `q002. In the preceding example we saw that the x and y displacement from from (2,3) to (9,14) are 9-2 = 7 and 14-3 = 11. Sketch an arrow which originates at (2,3) and terminates at (9,14), with the point of the arrow at the terminating end. If we were to sketch a geometrically similar arrow, having the same slope, orientation and length as the preceding, but starting at the point (-2, 5) at what point would the arrow terminate? Note that we can and should really incorporate information from the physics introductory problems.

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RESPONSE --> (5, 16)

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13:17:16 Originating at (-2,5) the arrow will displace 7 units in the x direction and 11 units in the y direction. Starting at x = -2 the arrow will displace 7 units in the x direction to end up at x = -2 + 7 = 5. Starting at y = 5 the arrow will displace 11 units in the y direction and end up at y = 5 + 11 = 16. The arrow therefore originates at (2,-5) and terminates at (5, 16). If we sketch the same arrow starting from the point (-2, 5) then it will again displace 7 units in the x direction, ending up at x = -2 + 7 = 5, and 11 units in the y direction, ending up at y = 5 + 11 = 16. As shown in Figure 58 the arrow terminates at the point (5, 16).

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RESPONSE --> check

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13:19:08 `q003. We say that the displacement of 7 units in the x direction and 11 units in the y direction is a vector, represented by the arrows used in the preceding problems and denoted using 'pointy braces' as < 7, 11 >. If we apply this vector, starting this time at the origin, at what point do we end up?

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RESPONSE --> (7, 11)

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13:19:44 As shown in Figure 40 this vector takes us from the origin (0,0) to the point (7, 11).

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RESPONSE --> check

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13:26:31 `q004. If we start from the terminal point of the vector in the preceding exercise and sketch a new vector having x displacement 3 and y displacement -8, at what point do we end up? Sketch the arrows representing these two vectors, the first running from (0,0) to (7,11) and the second from that point to its terminal point. Now sketch a vector from directly from (0,0) to the terminal point of the second vector. How can the x displacement of this new vector be calculated from the x displacements of the first two vectors? Answer the same question for the y coordinates.

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RESPONSE --> (10, 3) The sum of the x displacement The sum of the y displacement

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13:26:47 As shown in figure 11, the second vector runs from (7, 11) to (7 + 3, 11 + (-8) ) = (10, 3). The vector from the initial point of the first vector to the terminal point of the second therefore runs from (0, 0) to (10, 3), as shown in Figure 72. It should be clear from the calculations done above and from the sketches that the x displacement of the new vector is calculated by adding the x displacements of the original two vectors, and that the same strategy works for the y displacements.

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RESPONSE --> check

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13:30:43 `q005. In what sense can we say that the vector <10,3> is the sum of the two vectors <7, 11> and <3, -8>?

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RESPONSE --> the sum of the x and y displacement results in a third vector

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13:33:31 The x coordinate of the new vector to is 10, which is the sum 7 + 3 of the x coordinates of the two vectors. The y coordinate of the new vector is 3, the sum 11 + (-8) of the y coordinate of the two vectors. In this respect it is the sum.

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RESPONSE --> check, this will only work when a reference is the origin. The vector will be the same, but you would need a reference coordinate.

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13:38:25 `q006. http://164.106.222.236/ph1introsets/default.htm and choose Set 5, Vectors. Click in turn on Problems 1 - 9 and see if you can solve these problems. Solutions are given and are generalized and many are accompanied by figures. If you can't immediately solve them, study the solutions and learn to solve them. Explain the solution to the first problem.

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RESPONSE --> because the length (4) can be thought of as a hypotenuse of a right triangle, the 4 sin(64) = y because sin is y/hypotenuse. The same process for x using cosine is used to find distance.

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13:41:32 In case clarification is needed, displacement is just movement through a distance and in a certain direction. The vector (3, -8) of the preceding problem (and figur 72) corresponds to a displacement of 3 units in the x direction and -8 units in the y direction.

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RESPONSE --> q006. http://164.106.222.236/ph1introsets/default.htm and choose Set 5, Vectors. Click in turn on Problems 1 - 9 and see if you can solve these problems. Solutions are given and are generalized and many are accompanied by figures. If you can't immediately solve them, study the solutions and learn to solve them. Explain the solution to the first problem. I'm slightly confused on your answer to this question.

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Your work on this assignment is good. The confusion on that last answer is noted, but I believe you understand what's going on here very well, and I don't anticipate that you're going to have any trouble with the related text problems.

Let me know if you have questions.