#$&* course Mth 164 uestion: `q001. Sketch the points (2,3) and (9,14) on a set of coordinate axes. Give the x and the y displacements from (2,3) to (9,14).
.............................................
Given Solution: `aAs shown in Figure 75, the x displacement is from 2 to 9, a displacement of 9 - 2 = 7, while the y displacement is from 3 to 14, a displacement of 14 - 3 = 11. The arrows represent the direction of the displacements, from the initial point (2, 3) to the terminal point (9, 14).  &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*Ok ********************************************* 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: If we start out at (-2,5) the arrow will move 7 over in the x direction and 11 in the y. By starting at x = -2 and moving 7 it will be x = -2 + 7 = 5. Using y starting at 5 and moving 11 we will get 5 + 11 = 16. So this means it will end at (5,16). confidence rating #$&*2.5 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: `aOriginating at (-2,5) the arrow will displace 7 units in the x direction and 11 units in the y direction. Starting at x = -2 the arrow will displace 7 units in the x direction to end up at x = -2 + 7 = 5. Starting at y = 5 the arrow will displace 11 units in the y direction and end up at y = 5 + 11 = 16. The arrow therefore originates at (2,-5) and terminates at (5, 16). If we sketch the same arrow starting from the point (-2, 5) then it will again displace 7 units in the x direction, ending up at x = -2 + 7 = 5, and 11 units in the y direction, ending up at y = 5 + 11 = 16. As shown in Figure 58 the arrow terminates at the point (5, 16).  &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*Ok ********************************************* 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: Well if we are moving with that vector and starting at the origin of (0,0) we will end up at the point (7,11). confidence rating #$&*2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: As shown in Figure 40 this vector takes us from the origin (0,0) to the point (7, 11).  &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*Ok ********************************************* 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 start out with it running to (7,11) and end up with have (7 +3, 11-8) = (10, 3) confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: `aAs shown in figure 11, the second vector runs from (7, 11) to (7 + 3, 11 + (-8) ) = (10, 3). The vector from the initial point of the first vector to the terminal point of the second therefore runs from (0, 0) to (10, 3), as shown in Figure 72. It should be clear from the calculations done above and from the sketches that the x displacement of the new vector is calculated by adding the x displacements of the original two vectors, and that the same strategy works for the y displacements.  &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*Ok ********************************************* 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: We can say sum in the sense that we added the x and y coordinates together to get the new ones. For example we did 7 + 3 to get our x coordinate of 10 and the same for 11 and -8 to find our y coordinate. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: `aThe x coordinate of the new vector to is 10, which is the sum 7 + 3 of the x coordinates of the two vectors. The y coordinate of the new vector is 3, the sum 11 + (-8) of the y coordinate of the two vectors. In this respect it is the sum. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*Ok ********************************************* 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: We can use the angle given to determine the values of the x and y but just using the sin and cos functions the x value will use the cos: 5cos(63)= 2.3 the y value will use the sin: 5sin(63)= 4.5 "