I. Model Problems. II. Vector Basics III. Addition Of Vectors IV. Find Resultant Magnitude V. Find Angle associated with Resultant VI.

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1 On Twitter: twitter.com/mathprintables I. Model Problems. II. Vector Basics III. Addition Of Vectors IV. Find Resltant Magnitde V. Find Angle associated with Resltant VI. Answer Key Web Resorces Vectors : Resltant Vectors : All Rights Resered Commercial Use Prohibited Terms of Use: By downloading this file yo are agreeing to the Terms of Use Described at Online Graphing Calclator : Free Printable Math Worksheets

2 Vectors represent magnitde and direction. Vectors can be named like a ray, or in bold with one letter in bold, (or in handwritten text). The magnitde of ector is the size of a ector often representing force or elocity. The direction of a ector is an angle measrement where 0 is to the right on the horizontal Directio n I. Model Problems In the following problem yo will learn to show ector addition sing the tail-to-tip method. Find. Translate. Slide along so that the tail of is at the tip of Draw the resltant ector,, which starts at the tail of and ends at the tip of

3 In the following problem yo will find the magnitde and direction of a resltant ector. Problem: Sketch the ectors. A ector has a magnitde of 10 and a direction of 0. A ector has a magnitde of 6 and a direction of 50. Find the direction and magnitde of to the nearest whole ales. 50 Translate and draw the resltant. 6 Find the spplementary angle to find an angle of the triangle. Use Law of Cosines to find the magnitde, m, of. Law of Cosines Sbstitte. Simplify. Ѳ Ѳ Label with new information. Rond Use Law of Sines to find the direction, Ѳ, of. Law of Sines Sbstitte. Isolate. Ѳ Find the inerse. Rond to the nearest whole degree.

4 has a magnitde of 15 and a direction of 18. In the following problems yo will find information abot the resltant ector of two forces applied to an object Problem: Two forces with magnitdes of 15 ponds and 35 ponds are applied to an object. The magnitde of the resltant is 28 ponds. Find the measrement of the angle between the resltant ector and the ector of the 15 pond force to the nearest whole degree. Sketch the problem. Remember this is 15 lb Ѳ a sketch. The 28 lb actal angles may 15 lb 35 lb look ery different. 35 lb Law of Cosines Sbstitte. Simplify. Isolate. Find the inerse. Rond to the nearest degree. Problem: Sketch the problem. Remember this is a sketch. The actal angles may look ery different. Two forces with magnitdes of 15 ponds and 35 ponds and an angle of 40 between them are applied to an object. Find the magnitde of the resltant ector. 15 lb lb 15 lb lb 140 m Law of Cosines Sbstitte. Simplify. lb

5 II. Vector Basics 1. What is the magnitde and direction of 2. What is the magnitde and direction of 8.5 B 4.5 lb R 110 A 28 T 3. What is the magnitde and direction of 4. Sketch the resltant ector. J 12 lb 70 K Sketch the resltant ector. 6. Sketch the resltant ector What is the magnitde and direction of the resltant in the sketch below 8. What is the magnitde and direction of the resltant in the sketch below What is the magnitde and direction of the resltant in the sketch below

6 III. Addition of Vectors 10. Vector has a magnitde of 20 and a direction of 0. Vector has a magnitde of 40 and a direction of 60. Find the magnitde and direction of the resltant to the nearest whole 11. Vector has a magnitde of 15 and a direction of 0. Vector has a magnitde of 18 and a direction of 70. Find the magnitde and direction of the resltant to the nearest whole Vector has a magnitde of 24 and a direction of 0. Vector has a magnitde of 40 and a direction of 115. Find the magnitde and direction of the resltant to the nearest whole (contined on next page)

7 IV. Find the magnitde of the resltant ector when two forces are applied to an object. 13. Two forces with magnitdes of 20 ponds and 14 ponds and an angle of 55 between them are applied to an object. Find the magnitde of the resltant ector to the nearest whole 14. Two forces with magnitdes of 48 ponds and 65 ponds and an angle of 80 between them are applied to an object. Find the magnitde of the resltant ector to the nearest whole 20 lb lb 65 lb lb 15. Two forces with magnitdes of 70 ponds and 40 ponds and an angle of 130 between them are applied to an object. Find the magnitde of the resltant ector to the nearest whole 16. Two forces with magnitdes of 77 ponds and 45 ponds and an angle of 43 between them are applied to an object. Find the magnitde of the resltant ector to the nearest whole 17. Two forces with magnitdes of 62 ponds and 62 ponds and an angle of 145 between them are applied to an object. Find the magnitde of the resltant ector to the nearest whole

8 V. Find the angle measrements between the resltant ector and force ector when two forces are applied to an object. 18. Two forces with magnitdes of 15 ponds and 10 ponds are applied to an object. The magnitde of the resltant is 24 ponds. Find the measrement of the angle between the resltant ector and the ector of the 10 pond force to the nearest whole degree. 19. Two forces with magnitdes of 6 ponds and 18 ponds are applied to an object. The magnitde of the resltant is 13 ponds. Find the measrement of the angle between the resltant ector and the ector of the 18 pond force to the nearest whole degree. 20 lb 14 lb 18 lb 14 lb 20 lb 24 lb 18 lb 6 lb 6 lb 13 lb 20. Two forces with magnitdes of 45 ponds and 62 ponds are applied to an object. The magnitde of the resltant is 100 ponds. Find the measrement of the angle between the resltant ector and the ector of the 45 pond force to the nearest whole degree. 21. Two forces with magnitdes of 200 ponds and 340 ponds are applied to an object. The magnitde of the resltant is 150 ponds. Find the measrement of the angle between the resltant ector and the ector of the 200 pond force to the nearest whole degree. 22. Two forces with magnitdes of 40 ponds and 42 ponds are applied to an object. The magnitde of the resltant is 31ponds. Find the measrement of the angle between the resltant ector and the ector of the 42 pond force to the nearest whole degree.

9 V. Challenge Problems 23. Vector has a magnitde of 53 and a direction of 0. Vector has a magnitde of 10 and a direction of 295. Find the magnitde and direction of the resltant to the nearest whole 24. Vector has a magnitde of 27 and a direction of 40. Vector has a magnitde of 34 and a direction of 58. Find the magnitde and direction of the resltant to the nearest whole 18 lb Use ectors to answer the following qestions. a) If two forces from different directions are applied to an object, can the magnitde of the resltant be larger than the sm of the magnitdes of the forces? Jstify yor answer. b) What if the forces were from the same direction? Jstify yor answer.

10 VI. Answers , lb, lb, , , , , , , lb lb lb lb lb , , a) No, the sm of two sides is greater than the third therefore the magnitde of the resltant is less than the sm of the two forces. b) The magnitde of the resltant is eqal the sm of the two forces.