Vectors How do vectors combine into a resultant

Vector Diagrams • Vector diagrams are diagrams which depict the direction and relative magnitude of a vector quantity by a vector arrow

Vectors: Motion • the size of the velocity vector is increasing, so the diagram is depicting a motion with increasing velocity

Scalars and Vectors • Scalars are quantities which are fully described by a magnitude alone. • Vectors are quantities which are fully described by both a magnitude and a direction

Distance and Displacement • Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion. • Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position

Graphical (Scale method) and Analytical (Pythagorean) • • C 2=a 2+b 2 C 2 = (11 km) 2 + (11 km) 2 C 2 = 242 km 2 C = 15. 6 km

Example Vector Problem • A motorboat heads due east at 16 m/s across a river that flows due north at 9. 0 m/s. • What is the resultant velocity of the boat? • If the river is 136 m wide, how long does it take the motorboat to reach the other side?

Solution : Graphical Method • What is the resultant velocity of the boat?

Solution: Calculation of time • If the river is 136 m wide, how long does it take the motorboat to reach the other side? • V = d/t • 18 m/s = 136 m t • t = 7. 56 s

Trigonometric Method • Using the relationship of angles and Trigonometric functions to determine the magnitude of the vectors

Example Problem: Trigonometry • Determine the components of a 20 m displacement 300 northwest. • “a” west component and • “b” north component.

Solution Trigonometry • By choosing the proper component, • a: opposite • b: adjacent • c: resultant • Solve for each component

Summary • Vector addition problems may be solved by 2 methods: • Graphical • Analytical (Pythagorean) • Graphical method depends on a scale and use of angular measurements • Analytical method will use the formulas: • c 2 = a 2 + b 2 • Trigonometry