Vector and Vector Addition PDF

Vector and Vector Addition General Physics 1 Learning Objectives: differentiate vector and scalar quantities; perform addition of vectors graphically and analytically by using the component method; display awareness of the uses of vectors in different fields like technology an...

Vector and Vector Addition General Physics 1 Learning Objectives: differentiate vector and scalar quantities; perform addition of vectors graphically and analytically by using the component method; display awareness of the uses of vectors in different fields like technology and engineering. Scalar quantities are fully described by a magnitude (size or numerical value) only. While vector quantities give both the magnitude and direction. Vectors can be represented by the use of an arrow with a head and a tail. The length of the arrow represents the magnitude of the vector while the direction of the arrowhead represents the direction of the vector. The tail is called the initial point or the origin of the vector. The component method is a more convenient and accurate way to add vectors. In this method the x and y components of each vector are determined. The x component is the projection of the vector on the x-axis and the y component is the projection on the y-axis. Examples  Graphical Method Examples Use the graphical method to find the total displacement of a person who walks the following three paths on a flat field. First, she walks 25.0 m in a direction 49.0º north of east. Then, she walks 23.0 m heading 15.0º north of east. Finally, she turns and walks 32.0 m in a direction 68.0° south of east. Answer:  Analytical Method Example Matthew leaves the base camp and hikes 11 km, north and then hikes 11 km east. Determine Matthew's resulting displacement Answer:  Analytical Method Example Jomar rode his bicycle in the eastern direction for 5 meters. After that, he went 3 meters in a direction of 30° North of East. Determine Jomar’s displacement. Answer:  Component Method Examples: Emma went outside to jog. She jogged in the eastern direction for 5 meters, then she jogged 7 meters, 30° North of East. After that, she went 3 meters to the North and lastly, jogged 4 meters, 20° West of North. Find the displacement from her initial position to her final position. Answer: 5m, 0 east +5 0 +6.06 3.5 0 3 -3.76 1.37  Component Method Examples Use the component method to find the total displacement of a person who walks the following three paths on a flat field. First, she walks 25.0 m in a direction 49.0º north of east. Then, she walks 23.0 m heading 15.0º north of east. Finally, she turns and walks 32.0 m in a direction 68.0° south of east. QUIZ 1.2 Learning Objectives: interpret the displacement and velocity, respectively, as areas under a velocity vs. time and acceleration vs. time curve; convert a verbal description of a physical situation involving uniform acceleration in one dimension into mathematical description; and appreciate the importance of the mathematical description of a physical situation involving uniform acceleration in one dimension to road safety. Distance and Displacement General Mathematics Example: Quiz 1.2