10.2 Vectors in the Plane

Quick Review

What you’ll learn about Two-Dimensional Vectors Vector Operations Modeling Planar Motion Velocity, Acceleration, and Speed Displacement and Distance Traveled Essential Question How does the mathematics of vectors help us jump from one to two dimensions (and eventually higher)?

Two-Dimensional Vectors

Magnitude of a Vector Direction Angle of a Vector Head Minus Tail (HMT) Rule

Example Finding Magnitude and Direction 1.Find the magnitude and the direction angle  if the vector v =

Example Finding Magnitude and Direction 2. Find the component form of the vector with the given magnitude that forms the given directional angle with the positive x-axis.

Vector Addition and Scalar Multiplication

Performing Operations on Vectors

Properties of Vector Operations

Example Finding Ground Speed and Direction 3.

Velocity, Speed, Acceleration, and Direction of Motion

Displacement and Distance Traveled Suppose a particle moves along a path in the plane so that its velocity at any time t is where v 1 and v 2 are integrable functions of t. The displacement from t = a to t = b is given by the vector The preceding vector is added to the position at t = a to get the position at t = b. The distance traveled from t = a to t = b is

Example Finding Displacement and Distance Traveled 4. A particle moves in the plane with velocity vector At t = 0, the particle is at the point (1, 5). a. Find the position of the particle at t = 4.

Example Finding Displacement and Distance Traveled 4. A particle moves in the plane with velocity vector At t = 0, the particle is at the point (1, 5). b. What is the total distance traveled by the particle from t = 0 to t = 4?

Pg. 545, 10.2 #1-47 odd