MCV4U Vectors Lesson Assignment 6 In this assignment you are going to focus on: working with cartesian vectors Total Marks: 118 marks Instructions: After completing the lesson action section of your home page, you are ready to complete your lesson assignment. Follow these steps. a) In the textbox given, explain the strategy that you used to determine your answer. b) Fill in your answer. The mark for each question is given at the introduction to the questions to be completed. c) When finished answering all your questions, save your file and upload the file into the appropriate dropbox. Part A (Terminology): Matching (20 marks) Using your readings, match each term with the correct definition provided. The name of the term is given in the table and the definitions are listed below. Match the name of the term and the corresponding definition. As part of your answer, identify the sources of your information. Each question is worth 2 marks. - one for the matching and one mark for your proof. Match the vector coordinates to each Cartesian vector. D B H -4 2 4 K C -2 -4 a. [3, -4] d. [3, 2] b. [-2, 6] e. [5, 0] c. [4, 3] 1 . AB 2. MCV4U Lesson Assignment 6 Page 1 3. GH 4. JK 5. MN Match the magnitudes to their Cartesian vectors. yt U 2 R -4 4 x PO 21 X W a. 5 d. 2~/2 b. 10 e. 1 C. 10MCV4U Vectors Lesson Assignment 6 In this assignment you are going to focus on: working with cartesian vectors Total Marks: 118 marks Instructions: After completing the lesson action section of your home page, you are ready to complete your lesson assignment. Follow these steps. a) In the textbox given, explain the strategy that you used to determine your answer. b) Fill in your answer. The mark for each question is given at the introduction to the questions to be completed. c) When finished answering all your questions, save your file and upload the file into the appropriate dropbox. Part A (Terminology): Matching (20 marks) Using your readings, match each term with the correct definition provided. The name of the term is given in the table and the definitions are listed below. Match the name of the term and the corresponding definition. As part of your answer, identify the sources of your information. Each question is worth 2 marks. - one for the matching and one mark for your proof. Match the vector coordinates to each Cartesian vector. D B H -4 2 4 K C -2 -4 a. [3, -4] d. [3, 2] b. [-2, 6] e. [5, 0] c. [4, 3] 1 . AB 2. MCV4U Lesson Assignment 6 Page 1 3. GH 4. JK 5. MN Match the magnitudes to their Cartesian vectors. yt U 2 R -4 4 x PO 21 X W a. 5 d. 2~/2 b. 10 e. 1 C. 106. PC 7. RS TU 9. VW MCV4U Lesson Assignment 6 Page 2 10. XY Part B (Putting the Concepts to Work): Completion ( 98 marks): Using your reading, answer the following questions: For each question you are asked to: a) identify the information given in the question using a diagram b) determine the appropriate formula. c) substitute the values given into the formula and find the solution. d) give the final answer. e) as part of your answer, give the page number in the reference material or the website that you used to find the answer to the question. 1. If a = [1, 2] and b = [2, 7], find a + 2b .(five marks) a. 3 10 c. [5, 16] b. [6, 18] d. 281 2. If & = [-3, 2] and d = [2, -4], find - 2 + 3d .(five marks) a. [3, -10] C. 5 b. 277 d. [9, -14]6. PC 7. RS TU 9. VW MCV4U Lesson Assignment 6 Page 2 10. XY Part B (Putting the Concepts to Work): Completion ( 98 marks): Using your reading, answer the following questions: For each question you are asked to: a) identify the information given in the question using a diagram b) determine the appropriate formula. c) substitute the values given into the formula and find the solution. d) give the final answer. e) as part of your answer, give the page number in the reference material or the website that you used to find the answer to the question. 1. If a = [1, 2] and b = [2, 7], find a + 2b .(five marks) a. 3 10 c. [5, 16] b. [6, 18] d. 281 2. If & = [-3, 2] and d = [2, -4], find - 2 + 3d .(five marks) a. [3, -10] C. 5 b. 277 d. [9, -14]3. If m = [-1, -1] and 7 = [1, 1], find [m - 2).(five marks) a. [-2, -2] C. 0 b. 0 d. 2~/2 4. A 10 N force is applied at 45 to the horizontal. Write this force as a Cartesian vector.(five marks) a. [10, 10] C. 10 10 2'N2 b. [10, 0] d. -10 -10 5. A 50 N force is applied at 250 to the vertical. Write this force as a Cartesian vector.(five marks) a. [50, 50] c. [45.32, 21.13] b. [0, 50] d. [21.13, 45.32] MCV4U Lesson Assignment 6 Page 4 6. A ship is on a heading of 050 at 30 knots. Write this velocity as a Cartesian vector. (five marks) a. [22.98, 19.28] [30, 30] b. [19.28, 22.98] d. [50, 30] 7. A ship is on a heading of 000 at 7 knots. Write this velocity as a Cartesian vector.(five marks)3. If m = [-1, -1] and 7 = [1, 1], find [m - 2).(five marks) a. [-2, -2] C. 0 b. 0 d. 2~/2 4. A 10 N force is applied at 45 to the horizontal. Write this force as a Cartesian vector.(five marks) a. [10, 10] C. 10 10 2'N2 b. [10, 0] d. -10 -10 5. A 50 N force is applied at 250 to the vertical. Write this force as a Cartesian vector.(five marks) a. [50, 50] c. [45.32, 21.13] b. [0, 50] d. [21.13, 45.32] MCV4U Lesson Assignment 6 Page 4 6. A ship is on a heading of 050 at 30 knots. Write this velocity as a Cartesian vector. (five marks) a. [22.98, 19.28] [30, 30] b. [19.28, 22.98] d. [50, 30] 7. A ship is on a heading of 000 at 7 knots. Write this velocity as a Cartesian vector.(five marks). [7, 7] C. [7, 0] b. [0, 7] d. [0, -7] 8. A ship is on a heading of 250 at 15 knots. Write this velocity as a Cartesian vector.(five marks) a. [-15, -15] c. [-12.99, 7.5] b. [-12.99, -7.5] d. [-7.5, -12.99] MCV4U Lesson Assignment 6 Page 5 9. A ship is on a heading of 270 at 10 knots. Write this velocity as a Cartesian vector. (five marks) a. [10, 0] [10, 10] b. [10, 270] d. [-10, 0] 10. A ship is on a heading of 040 at 20 knots and a 2 knot current is flowing from 010. Determine the resultant velocity of the ship, using Cartesian vectors, and state the magnitude and bearing of the resultant.(eight marks) 11. A ship is on a heading of 160 at 15 knots and an 8 knot current is flowing from 090. Determine the resultant velocity of the ship, using Cartesian vectors, and state the magnitude and bearing of the resultant. .(eight marks. [7, 7] C. [7, 0] b. [0, 7] d. [0, -7] 8. A ship is on a heading of 250 at 15 knots. Write this velocity as a Cartesian vector.(five marks) a. [-15, -15] c. [-12.99, 7.5] b. [-12.99, -7.5] d. [-7.5, -12.99] MCV4U Lesson Assignment 6 Page 5 9. A ship is on a heading of 270 at 10 knots. Write this velocity as a Cartesian vector. (five marks) a. [10, 0] [10, 10] b. [10, 270] d. [-10, 0] 10. A ship is on a heading of 040 at 20 knots and a 2 knot current is flowing from 010. Determine the resultant velocity of the ship, using Cartesian vectors, and state the magnitude and bearing of the resultant.(eight marks) 11. A ship is on a heading of 160 at 15 knots and an 8 knot current is flowing from 090. Determine the resultant velocity of the ship, using Cartesian vectors, and state the magnitude and bearing of the resultant. .(eight marks12. An airplane is on a heading of 075 at 250 km/h and an 85 km/h wind is blowing from 300. Determine the resultant velocity of the airplane, using Cartesian vectors, and state the groundspeed and bearing of the resultant. .(eight marks) 13. An airplane is on a heading of 235 at 600 km/h and a 110 km/h wind is blowing from due west. Determine the resultant velocity of the airplane, using Cartesian vectors, and state the groundspeed and bearing of the resultant. .(eight marks) MCV4U Lesson Assignment 6 Page 7 14. Two forces act on an object at an angle of 40 to each other. One force has a magnitude of 100 N and the other has a magnitude of 130 N. Determine the resultant force, using Cartesian vectors (let the 100-N force vector lie along the positive x-axis), and state the magnitude of the resultant and its direction. .(eight marks) 15. Two skaters push a person sitting in a chair along the ice. The forces exerted by the skaters are 200 N and 250 N at an angle of 20 to one another. Determine the resultant force of the skaters, using Cartesian vectors (let the 200-N force vector lie along the positive x-axis), and state the magnitude and direction of the resultant. (eight marks)12. An airplane is on a heading of 075 at 250 km/h and an 85 km/h wind is blowing from 300. Determine the resultant velocity of the airplane, using Cartesian vectors, and state the groundspeed and bearing of the resultant. .(eight marks) 13. An airplane is on a heading of 235 at 600 km/h and a 110 km/h wind is blowing from due west. Determine the resultant velocity of the airplane, using Cartesian vectors, and state the groundspeed and bearing of the resultant. .(eight marks) MCV4U Lesson Assignment 6 Page 7 14. Two forces act on an object at an angle of 40 to each other. One force has a magnitude of 100 N and the other has a magnitude of 130 N. Determine the resultant force, using Cartesian vectors (let the 100-N force vector lie along the positive x-axis), and state the magnitude of the resultant and its direction. .(eight marks) 15. Two skaters push a person sitting in a chair along the ice. The forces exerted by the skaters are 200 N and 250 N at an angle of 20 to one another. Determine the resultant force of the skaters, using Cartesian vectors (let the 200-N force vector lie along the positive x-axis), and state the magnitude and direction of the resultant. (eight marks)