Kinematics in Two Dimensions Vector Diagrams A vector

Kinematics in Two Dimensions

Vector Diagrams: § A vector has a tail and a tip. § The length of the line segment depends on the magnitude of the vector § Arrowhead indicates direction Tail Tip

§ Collinear vectors lie on the same straight line § Resultant Vector is a vector drawn from the tail of the first vector to the tip of the next tip tail Resultant tail tip

§ Vector Components are perpendicular parts into which a vector can be separated (x and y components) y-component x-component

Directions: §Can be expressed as an angle: § to the horizontal § from the positive xaxis § to the vertical § in terms of N, S, E, W

Cartesian Method: § Positive x-axis is at 0 o § Angles are measured by moving counterclockwise about the origin 150 o

Navigator Method: § Use compass bearing N, S, E, W 300 [30 o. N of W] or [W 30 o. N] [60 o. W of N] or [N 60 o. W]

Vector Addition: § Draw a vector diagram that is a reasonable representation and join tip to tail

(A) If Vectors are perpenicular to each other § Find the amount of the resultant vector (R) using Pythagoreans Theorem. § a 2 +b 2 = c 2 § Find the direction using trig. Functions: § Sine § Cosine § Tangent

Ex: The displacement of a airplane is 125 km [30. 0 o S of E]. Determine the x and y components.

Ex: If a student walks 62 m [E] then 73 m [N]. What is the total displacement?

Homework: § § § Vector Addition Worksheet Page 84 #1, 2 Page 90 #4, 5, 7