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Vectors

This guide explores the concept of vectors, focusing on their magnitude and direction. It provides examples such as locating a bag of candy with practical displacement instructions, illustrated using vector diagrams and scale representation. It also covers vector addition and the use of trigonometry to determine vector directions. Practice problems are included to reinforce understanding. By the end of this guide, you'll be equipped to calculate and visualize vectors in real-world scenarios, improving your grasp of this fundamental concept in physics.

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Vectors

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  1. Vectors

  2. Vectors • Has both Magnitude and Direction Example: “A bag of candy is located outside the classroom. To find it, displace yourself 20 meters.” What’s the problem?

  3. How about…“A bag of candy is located outside the classroom. To find it displace yourself from the center of the classroom door 20 meters in a direction 30 degrees to the west of north.”

  4. Vector Diagrams Scale Vector arrow Magnitude and direction 20 m, 30 degrees West of North

  5. Vectors are expressed as a counterclockwise angle of rotation

  6. Magnitude of a Vector Using the scale (1 cm = 5 miles), a displacement vector that is 15 miles will be represented by a vector arrow that is 3 cm in length. Similarly, a 25-mile displacement vector is represented by a 5-cm long vector arrow. And finally, an 18-mile displacement vector is represented by a 3.6-cm long arrow. See the examples shown below.

  7. Adding Vectors

  8. Example… Eric leaves the base camp and hikes 11 km, north and then hikes 11 km east. Determine Eric's resulting displacement.

  9. Practice A Answer R2 = (5)2 + (10)2 R2 = 125 R = 11.2 km

  10. Practice B Answer R2 = (30)2 + (40)2 R2 = 2500 R = 50 km

  11. Using Trig to Determine a Vector’s Direction

  12. Stupid Ways, Important Stuff Sin = o/h Cos = a/h Tan = o/a

  13. Remember the hiker problem from before?

  14. Practice A Tan Ɵ = (5/10) = 0.5 Ɵ= tan-1(0.5) Ɵ= 26.6 ° Direction of R = 90 °+ 26.6 ° Direction of R = 116.6 °

  15. Practice B Tan Ɵ = (40/30) = 1.333 Ɵ= tan-1 (1.333) Ɵ= 53.1 ° Direction of R = 180 °+ 53.1 ° Direction of R = 233.1 °

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