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{"ops":[{"insert":"1. Physical quantities are categorized as either scalar or vector. With clear examples, discuss the feature which differentiates them.\n2. Clearly explain the meaning of the term resultant vector.\n3. From Lecture theater 2, Mr. Nkonde moves 80m east along the sheltered walk path way and then 125m south to the university library. Find the displacement of Mr Nkonde.\n4. To go from the student hostels to the university library, a student must cover 650m in a direction 47o south of west. To go from the football ground to the library, the student must move straight south for 420m. How far and in what direction must the student move to go from hostels to the football ground?\n5. Mr. Kazhimaika gives a map to a first student studying Fisheries and Aquaculture so that she gets to the new fish ponds. The map says, \u2018start from the central administration car park, go 125m straight north, then 200m at 45o north of east, then 150m straight east, and finally, 30m at 30o east of south\u2019. How far from the central administration car park and in what direction are the fish ponds?\n6. In map \u2013 work exercise, hikers are required to walk from a tree mark A on the map to another marked B which lies 5.0km due east of A. The hikers then will have to walk in a straight line to a waterfall in position C which has a component measured from B of 2.0km east and 6.0km north.\n(i) Draw a clearly labeled displacement \u2013 vector diagram of the route the hikers would take to complete the journey.\n(ii) What would be the total distance to be covered by the hikers?\n\n7. Four forces, 60N at 60o and 50N at 30o both clockwise, 50N at 30o, 40N due north \u2013 west and 30N south \u2013 west, act at the origin. Calculate the magnitude and direction of the resultant force.\n\n8. The diagram below shows three ropes F1= 450N, F2= 300N and F3= 600N hooked from the same hook as they support the roof. Resolve each force acting on the hook into its x and y components.\n\n12. Determine the magnitudes of the following vectors;\n(i) \ud835\udc68\u20d7\u20d7 =(\ud835\udfd0\ud835\udc8a\u0302+\ud835\udfd1\ud835\udc8b\u0302+\ud835\udfd4\ud835\udc8c\u0302)\n(ii) \ud835\udc69\u20d7\u20d7 =(\ud835\udfd1\ud835\udc8a\u0302+\ud835\udfd7\ud835\udc8b\u0302\u2212\ud835\udfd4\ud835\udc8c\u0302)\n(iii) \ud835\udc6a\u20d7\u20d7 =(\ud835\udfd1\ud835\udc8a\u0302\u2212\ud835\udfd3\ud835\udc8b\u0302+\ud835\udc8c\u0302)\n(iv) \ud835\udc6b\u20d7\u20d7 =(\ud835\udfd6\ud835\udc8a\u0302\u2212\ud835\udfd2\ud835\udc8b\u0302+\ud835\udfd6\ud835\udc8c\u0302)\n\n13. Find the angle between the vectors \ud835\udc68\u20d7\u20d7 =(\ud835\udfd1\ud835\udc8a\u0302+\ud835\udfd0\ud835\udc8b\u0302+\ud835\udc8c\u0302) and \ud835\udc68\u20d7\u20d7 =(\ud835\udfd3\ud835\udc8a\u0302\u2212\ud835\udfd0\ud835\udc8b\u0302\u2212\ud835\udfd1\ud835\udc8c\u0302)\n14. Prove that following vectors are perpendicular to each other\n(i) \ud835\udc68\u20d7\u20d7 =(\ud835\udc8a\u0302+\ud835\udfd0\ud835\udc8b\u0302+\ud835\udfd1\ud835\udc8c\u0302) and \ud835\udc69\u20d7\u20d7 =(\ud835\udfd0\ud835\udc8a\u0302\u2212\ud835\udc8b\u0302)\n(ii) \ud835\udc6a\u20d7\u20d7 =(\ud835\udfd1\ud835\udc8a\u0302\u2212\ud835\udfd0\ud835\udc8b\u0302+\ud835\udfd6\ud835\udc8c\u0302) and \ud835\udc6b\u20d7\u20d7 =(\ud835\udfd0\ud835\udc8a\u0302+\ud835\udfd0\ud835\udc8b\u0302\u2212\ud835\udfcf\ud835\udfd2\ud835\udc8c\u0302)\n(iii) \ud835\udc6c\u20d7\u20d7 =(\ud835\udfcf\ud835\udfd6\ud835\udc8a\u0302+\ud835\udfd4\ud835\udc8b\u0302+\ud835\udfd4\ud835\udc8c\u0302) and \ud835\udc6d\u20d7\u20d7 =(\u2212\ud835\udfd0\ud835\udc8a\u0302+\ud835\udfd1\ud835\udc8b\u0302+\ud835\udfd1\ud835\udc8c\u0302)\n(iv) \ud835\udc6e\u20d7\u20d7 =(\u2212\ud835\udfd4\ud835\udc8a\u0302+\ud835\udfd1\ud835\udfd2\ud835\udc8c\u0302) and \ud835\udc6f\u20d7\u20d7\u20d7 =(\ud835\udfcf\ud835\udfd0\ud835\udc8a\u0302+\ud835\udfd0\ud835\udfd1\ud835\udc8b\u0302+\ud835\udfd2\ud835\udc8c\u0302)\n\n15. Determine the value of a so that vector \ud835\udc68\u20d7\u20d7 =(\ud835\udfcf\ud835\udfce\ud835\udc8a\u0302+\ud835\udfcf\ud835\udfd2\ud835\udc8b\u0302\u2212\ud835\udfd4\ud835\udc8c\u0302) is perpendicular to vector \ud835\udc68\u20d7\u20d7 =(\ud835\udfcf\ud835\udfd0\ud835\udc8a\u0302+\ud835\udfcf\ud835\udfd0\ud835\udc8b\u0302+\ud835\udc82\ud835\udc8c\u0302)\n\n16. A particle covers a distance of (\ud835\udfd0\ud835\udc8a\u0302+\ud835\udfd1\ud835\udc8b\u0302+\ud835\udfd3\ud835\udc8c\u0302) metres in the direction of a constant force of (\ud835\udfd5\ud835\udc8a\u0302+\ud835\udfd6\ud835\udc8b\u0302+\ud835\udfd1\ud835\udc8c\u0302) newtons acting on it. Calculate the work done by the force on this particle.\n\n17. A body moves from position (\ud835\udfd0\ud835\udc8a\u0302+\ud835\udfd0\ud835\udfce\ud835\udc8b\u0302\u2212\ud835\udfcf\ud835\udfd6\ud835\udc8c\u0302) metres to a position\n(\ud835\udfcf\ud835\udfd4\ud835\udc8a\u0302+\ud835\udfd0\ud835\udfd2\ud835\udc8b\u0302+\ud835\udfcf\ud835\udfd3\ud835\udc8c\u0302) metres when a force of (\ud835\udfd2\ud835\udc8a\u0302+\ud835\udfd0\ud835\udc8b\u0302+\ud835\udfd1\ud835\udc8c\u0302) newton is applied on it. Calculate the work done on a body.\n\n18. A point of application of a force \ud835\udc6d\u20d7\u20d7 =(\ud835\udfcf\ud835\udfd4\ud835\udc8a\u0302+\ud835\udfd0\ud835\udfce\ud835\udc8b\u0302+\ud835\udfcf\ud835\udfd3\ud835\udc8c\u0302) is moved from\n\ud835\udc93\ud835\udfcf\u20d7\u20d7\u20d7\u20d7 =(\ud835\udfd0\ud835\udc8a\u0302+\ud835\udfd5\ud835\udc8b\u0302+\ud835\udfd0\ud835\udc8c\u0302) to \ud835\udc93\ud835\udfd0\u20d7\u20d7\u20d7\u20d7 =(\ud835\udfd3\ud835\udc8a\u0302+\ud835\udfcf\ud835\udfd0\ud835\udc8b\u0302+\ud835\udfd1\ud835\udc8c\u0302). Find the work done.\n"}]}

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