#$&* course mth 164 10/30 5pm 009. VectorsGoals for this Assignment include but are not limited to the following:
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Given Solution: `aAs shown in Figure 75, the x displacement is from 2 to 9, a displacement of 9 - 2 = 7, while the y displacement is from 3 to 14, a displacement of 14 - 3 = 11. The arrows represent the direction of the displacements, from the initial point (2, 3) to the terminal point (9, 14). &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q002. In the preceding example we saw that the x and y displacement from from (2,3) to (9,14) are 9-2 = 7 and 14-3 = 11. Sketch an arrow which originates at (2,3) and terminates at (9,14), with the point of the arrow at the terminating end. If we were to sketch a geometrically similar arrow, having the same slope, orientation and length as the preceding, but starting at the point (-2, 5) at what point would the arrow terminate? Note that we can and should really incorporate information from the physics introductory problems. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The point would be (5, 16). Start at (-2, 5) move 7 points to the right then move up 11 points to get the new point. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aOriginating 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). &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `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? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: We would be at point (7, 11) confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: As shown in Figure 40 this vector takes us from the origin (0,0) to the point (7, 11). &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q004. If we start from the terminal point of the vector in the preceding exercise and sketch a new vector having x displacement 3 and y displacement -8, at what point do we end up? Sketch the arrows representing these two vectors, the first running from (0,0) to (7,11) and the second from that point to its terminal point. Now sketch a vector from directly from (0,0) to the terminal point of the second vector. How can the x displacement of this new vector be calculated from the x displacements of the first two vectors? Answer the same question for the y coordinates. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: We would add the x displacements to get 10, then add the y displacements to get 3. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aAs 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. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q005. In what sense can we say that the vector <10,3> is the sum of the two vectors <7, 11> and <3, -8>? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Because 7 + 3 = 10 for the x coordinate, and 11 + -8 = 3 for the y coordinate. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aThe x coordinate of the new vector to is 10, which is the sum 7 + 3 of the x coordinates of the two vectors. The y coordinate of the new vector is 3, the sum 11 + (-8) of the y coordinate of the two vectors. In this respect it is the sum. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q006. Access the site http://vhmthphy.vhcc.edu/ph1introsets/default.htm and choose Set 5, Vectors. Click in turn on Problems 1 - 9 and see if you can solve these problems. Solutions are given and are generalized and many are accompanied by figures. If you can't immediately solve them, study the solutions and learn to solve them. Explain the solution to the first problem. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: To find the x coordinate we have the length of the vector multiplied by cosine (theta). To find the y coordinate we have the length of the vector multiplied by sine (theta). confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aIn 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. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aThis completes this q_a_. Click once more for a message on completing the remainder of this assignment. Complete Assignment 9, including Class Notes, text problems and Web-based problems as specified on the Assts page. When you have completed the entire assignment run the Query program. Submit SEND files from Query and q_a_. end program 001. Radian measure and the unit circle. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aGoals for this Assignment include but are not limited to the following: 1. Know the definition of the radian. 2. Relate coordinate positions on the unit circle to angular displacement and to arc displacement. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: