Working with Vectors

What’s a vector? It is a physical quantity that has both magnitude (size) and direction. Examples: velocity v displacement d acceleration a

Direction Convention North or up (the page) East or West or right left South or down (the page)

Working with Vectors Vectors are drawn as arrows. The arrow designates the direction of motion, force or flow. The length corresponds to the magnitude of the quantity. v = 60 m/s East

Adding Vectors Graphical addition: A + B Drawn tip to tail to add Drawn to scale C B A

Adding Vectors Graphical addition: A + B = C The resultant vector, C, is drawn from the tail of the first vector to the tip of the last C B A

Example1: Adding Parallel Vectors Sue drove 2 mile east to pick up her friend Sam for school. She continued on for another 1 miles east to school. How far was Sue from her home? Draw the first vector indicating magnitude and direction 2 miles east 1 mile east Draw the second vector beginning at the tip of the first

Example1: Adding Parallel Vectors Sue drove 1 mile east to pick up her friend Sam for school. She continued on for another 2 miles east to school. How far was Sue from her home? Draw the resultant from the tail of the starting vector to the tip of the final vector. 3 miles east 2 miles east 1 mile east

Example2: Adding Parallel Vectors Irene drove 3 miles east McDonalds for lunch. She then drove 1 mile west to get back to school. How far was Irene from her home? 1 mile west 3 miles east

Example2: Adding Parallel Vectors Irene drove 3 miles east McDonalds for lunch. She then drove 1 mile west to get back to school. How far was Irene from her home? 2 miles east 1 mile west 3 miles east

Example 2: Adding Vectors Jenny drove 2 miles east to pick up her friend Michelle for school. They drove north 1 mile to pick up John. How far was Jenny from her home? Draw the first vector to scale. (example:1 m = 1 mile). 2 miles east

Example 3: Adding Vectors Jenny drove 2 miles east to pick up her friend Michelle for school. They drove north 1 mile to pick up John. How far was Jenny from her home? Measure the angle and draw the next vector to scale starting at the tip of the last. 1 mile north 90 degrees 2 miles east

Example 3: Adding Vectors Draw the resultant from the tail of the starting vector to the tip of the final vector. Measure the length. Use your scale to determine the actual distance. Measure the angle to determine the direction. 2.2 miles north east 1 mile east 90 deg 26 deg 2 miles east

Adding Multiple Vectors Same process – Many vectors. D C Measure the length R B Measure the angle A