Vectors and Projectile Motion Notes ThE tEtErS （向量和抛物运动tEtErS笔记）.pdf

Vectors and Projectile Motion Notes When you use an arrow to represent a vector quantity its length represents the magnitude and the arrow points in the direction of the vector quantity. Look at the arrows below: the top arrow could represent a displacement of 10 meters to the east. Based on that knowledge the middle arrow, which is twice as long as the top arrow, would represent 20 meters to the east. The bottom arrow would also represent 20 meters, but to the west. The arrow pointing to the top of the page would represent 10 meters, since it is the same length as the top arrow, to the north. The arrow as used here is a vector and can be used to represent any vector quantity. Let’s use the arrows above to represent velocities. If the top arrow is 20 mi/h to the south, then the middle arrow would be 40 mi/h to the south. The bottom arrow is 40 mi/h north and the arrow pointing up is 20 mi/h to the east. What the arrow represents depends on how you define (set-up) the original vector representation. Once you have defined the original, all other arrows must be drawn to the same “scale”. If one centimeter on your paper represents 10 mi/h, then an arrow representing 80 mi/h must be eight centimeters long. If pointing right represents north, then pointing left must be south. Combining vector quantities graphically is often useful to help “picture” quantities that may seem abstract and not as straight forward. Consider a girl swimming with a velocity of 3 m/s downstream in a river. Her velocity can be represented with a vector three centimeters long. The velocity of the water in the river is 4 m/s. The river vector is River Girl 4 centimeters long. If we want to know how fast the girl is swimming relative to you watching on the side of the river, we can just combine the vectors. This combination, called the resultant is shown below the combined vectors. The resultant’s lengt